chap 009

Chapter 09One-Sample Hypothesis Tests

True / False Questions1.The level of significance refers to the probability of making a Type II error.TrueFalse

2.The level of significance refers to the probability of making a Type I error.TrueFalse

3.A simultaneous reduction in both and will require a larger sample size.TrueFalse

4.The probability of rejecting a false null hypothesis increases as the sample size increases, other things being equal.TrueFalse

5.When the probability of a Type I error increases, the probability of a Type II error must decrease, ceteris paribus.TrueFalse

6.A false positive in a drug test for steroids is a Type II error.TrueFalse

7.If a judge acquits every defendant, the judge will never commit a Type I error (H0 is the hypothesis of innocence).TrueFalse

8.When your sample size increases, the chance of both Type I and Type II error will increase.TrueFalse

9.A Type II error can only occur when you fail to reject H0.TrueFalse

10.A Type I error can only occur if you reject H0.TrueFalse

11.John rejected H0 so we know definitely that he did not commit Type II error.TrueFalse

12.In hypothesis testing we cannot prove a null hypothesis is true.TrueFalse

13.For a given level of significance (), increasing the sample size will increase the probability of Type II error because there are more ways to make an incorrect decision.TrueFalse

14.For a given sample size, reducing the level of significance will decrease the probability of making a Type II error.TrueFalse

15.The probability of a false positive is decreased if we reduce .TrueFalse

16.A hypothesis test may be statistically significant, yet have little practical importance.TrueFalse

17.Compared to using = .01, choosing = .001 will make it less likely that a true null hypothesis will be rejected.TrueFalse

18.A two-tailed hypothesis test for H0: = 15 at = .10 is analogous to asking if a 90 percent confidence interval for contains 15.TrueFalse

19.For a given sample size and level, the Student's t value always exceeds the z value.TrueFalse

20.For a given level of significance, the critical value of Student's t increases as n increases.TrueFalse

21.For a sample of nine items, the critical value of Student's t for a left-tailed test of a mean at = .05 is -1.860.TrueFalse

22.Holding other factors constant, it is harder to reject the null hypothesis for a mean when conducting a two-tailed test rather than a one-tailed test.TrueFalse

23.If we desire = .10, then a p-value of .13 would lead us to reject the null hypothesis.TrueFalse

24.The p-value is the probability of the sample result (or one more extreme) assuming H0 is true.TrueFalse

25.The probability of rejecting a true null hypothesis is the significance level of the test.TrueFalse

26.A null hypothesis is rejected when the calculated p-value is less than the critical value of the test statistic.TrueFalse

27.In a right-tailed test, the null hypothesis is rejected when the value of the test statistic exceeds the critical value.TrueFalse

28.The critical value of a hypothesis test is based on the researcher's selected level of significance.TrueFalse

29.If the null and alternative hypotheses are H0: 100 and H1: > 100, the test is right-tailed.TrueFalse

30.The null hypothesis is rejected when the p-value exceeds the level of significance.TrueFalse

31.For a given null hypothesis and level of significance, the critical value for a two-tailed test is greater than the critical value for a one-tailed test.TrueFalse

32.For a given Ho and level of significance, if you reject the H0 for a one tailed-test, you would also reject H0 for a two-tailed test.TrueFalse

33.If the hypothesized proportion is 0 = .025 in a sample of size 120, it is safe to assume normality of the sample proportion p.TrueFalse

34.For a mean, we would expect the test statistic to be near zero if the null hypothesis is true.TrueFalse

35.In the hypothesis H0: = 0, the value of 0 is derived from the sample.TrueFalse

36.In testing the hypotheses H0: 0, H1: > 0, we would use a right-tailed test.TrueFalse

37.To test the hypothesis H0: = .0125 using n = 160, it is safe to assume normality of p.TrueFalse

38.In testing a proportion, normality of p can be assumed if n0 10 and n(1 - 0) 10.TrueFalse

39.Power is the probability of rejecting the null hypothesis when it is false and is equal to 1 - .TrueFalse

40.Other things being equal, a smaller standard deviation implies higher power.TrueFalse

41.The power of a test is the probability that the test will reject a false null hypothesis.TrueFalse

42.The height of the power curve shows the probability of accepting a true null hypothesis.TrueFalse

43.The power curve plots on the Y axis and the test statistic on the X axis.TrueFalse

44.A smaller probability of Type II error implies higher power of the test.TrueFalse

45.Varying the true mean is a movement along the power curve, not a shift in the curve.TrueFalse

46.Increasing the sample size shifts the power curve upward, ceteris paribus.TrueFalse

47.Increasing the level of significance shifts the power curve upward, ceteris paribus.TrueFalse

48.A power curve for a mean is at its lowest point when the true is very near 0.TrueFalse

49.Larger samples lead to increased power, ceteris paribus.TrueFalse

50.In graphing power curves, there is a different power curve for each sample size n.TrueFalse

51.In hypothesis testing, we are trying to reject the alternative hypothesis.TrueFalse

52.In hypothesis testing, we are trying to prove the null hypothesis.TrueFalse

53.When is unknown, it is more conservative to use z instead of t for the critical value.TrueFalse

Multiple Choice Questions54.For a given sample size, when we increase the probability of Type I error, the probability of a Type II error:

A.remains unchanged.

B.increases.

C.decreases.

D.is impossible to determine without more information.

55.After testing a hypothesis regarding the mean, we decided not to reject H0. Thus, we are exposed to:

A.Type I error.

B.Type II error.

C.Either Type I or Type II error.

D.Neither Type I nor Type II error.

56.After testing a hypothesis, we decided to reject the null hypothesis. Thus, we are exposed to:

A.Type I error.

B.Type II error.



57.Which statement about is not correct?

A.It is the probability of committing a Type I error.

B.It is the test's significance level.

C.It is the probability of rejecting a true H0.

D.It is equal to 1 - .

58.Which of the following is correct?

A.When sample size increases, both and may decrease.

B.Type II error can only occur when you reject H0.

C.Type I error can only occur if you fail to reject H0.

D.The level of significance is the probability of Type II error.

59.Which of the following is incorrect?

A.The level of significance is the probability of making a Type I error.

B.Lowering both and at once will require a higher sample size.

C.The probability of rejecting a true null hypothesis increases as n increases.

D.When Type I error increases, Type II error must decrease, ceteris paribus.

60.John rejected his null hypothesis in a right-tailed test for a mean at = .025 because his critical t value was 2.000 and his calculated t value was 2.345. We can be sure that:

A.John did not commit Type I error.

B.John did not commit Type II error.

C.John committed neither Type I nor Type II error.

D.John committed both Type I and Type II error.

61."My careful physical examination shows no evidence of any serious problem," said Doctor Morpheus. "However, a very costly lab test can be performed to check for the rare condition known as estomalgia fatalis. The test is almost invariably negative for persons with your age and symptoms. My personal hypothesis is that the occasional stomach pain you reported is due to indigestion caused by eating tacos with too much hot sauce. But you must decide for yourself." As you consider your doctor's hypothesis, what would be the consequence of Type I error on your part?

A.It can't be determined without knowing the type of test.

B.Your estomalgia fatalis will go undetected.

C.You will waste money on an unnecessary lab test.

D.Your survivors will enjoy a sizeable malpractice award.

62.Which of the following statements is correct?

A.Increasing will make it more likely that we will reject H0, ceteris paribus.

B.Doubling the sample size roughly doubles the test statistic, ceteris paribus.

C.A higher standard deviation would increase the power of a test for a mean.

D.The p-value shows the probability that the null hypothesis is false.

63."I believe your airplane's engine is sound," states the mechanic. "I've been over it carefully, and can't see anything wrong. I'd be happy to tear the engine down completely for an internal inspection at a cost of $1,500. But I believe that engine roughness you heard in the engine on your last flight was probably just a bit of water in the fuel, which passed harmlessly through the engine and is now gone." As the pilot considers the mechanic's hypothesis, the cost of Type I error is:

A.the pilot will experience the thrill of no-engine flight.

B.the pilot will be out $1,500 unnecessarily.

C.the mechanic will lose a good customer.

D.impossible to determine without knowing .

64.A study over a 10-year period showed that a certain mammogram test had a 50 percent rate of false positives. This indicates that:

A.about half the tests indicated cancer.

B.about half the tests missed a cancer that exists.

C.about half the tests showed a cancer that didn't exist.

D.about half the women tested actually had no cancer.

65.You are driving a van packed with camping gear (total weight 3,500 pounds including yourself and family) into a northern wilderness area. You take a "short cut" that turns into a one-lane road, with no room to turn around. After 11 miles you come to a narrow bridge with a faded sign saying "Safe Up to 2 Tons." About a half-mile ahead, you can see that your road rejoins the main highway. You consider the sign's hypothesis carefully before making a decision. The cost of Type I error is:

A.you pass safely over the bridge and everyone's happy.

B.about $23,900, not including medical bills.

C.you will find out just how cold that river actually is.

D.your kids will think you're a chicken.

66.After lowering the landing gear, the pilot notices that the "gear down and locked" light is not illuminated. "It's probably just a burned out light bulb," she says, as she proceeds on final approach for landing. Considering the pilot's hypothesis, which is the result of Type I error?

A.The sound of metal scraping on concrete will be heard upon landing.

B.The landing is delayed unnecessarily while the bulb and gear are checked.

C.We cannot be sure without knowing whether or not the bulb is actually faulty.

67.As you are crossing a field at the farm, your country cousin Jake assures you, "Don't worry about that old bull coming toward us. He's harmless." As you consider Jake's hypothesis, what would be Type I error on your part?

A.You will soon feel the bull's horns.

B.You will run away for no good reason.

C.Jake will not have any more visits from you.

68.Which is not true of p-values?

A.When they are small, we want to reject H0.

B.They measure the probability of an incorrect decision.

C.They show the chance of Type I error if we reject H0.

D.They do not require to be specified a priori.

69.For a test of a mean, which of the following is incorrect?

A.H0 is rejected when the calculated p-value is less than the critical value of the test statistic.

B.In a right-tailed test, we reject H0 when the test statistic exceeds the critical value.

C.The critical value is based on the researcher's chosen level of significance.

D.If H0: 100 and H1: > 100, then the test is right-tailed.

70.Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours. A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital and found a mean hospital stay of 40 hours with a standard deviation of 20 hours. "Aha!" she cried, "the average stay exceeds the guideline." At = .025, the critical value for a right-tailed test of her hypothesis is:

A.1.753

B.2.131

C.1.645

D.1.960

71.Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours. A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital and found a mean hospital stay of 40 hours with a standard deviation of 20 hours. "Aha!" she cried, "the average stay exceeds the guideline." The value of the test statistic for her hypothesis is:

A.2.080

B.0.481

C.1.866

D.2.000

72.Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours. A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital, and found a mean hospital stay of 40 hours with a standard deviation of 20 hours. "Aha!" she cried, "the average stay exceeds the guideline." The p-value for a right-tailed test of her hypothesis is:

A.between .05 and .10.

B.between .025 and .05.

C.between .01 and .025.

D.less than .01.

73.For a right-tailed test of a hypothesis for a population mean with n = 14, the value of the test statistic was t = 1.863. The p-value is:



C.greater than .10.

D.less than .01.

74.Hypothesis tests for a mean using the critical value method require:

A.knowing the true value of .

B.sampling a normal population.

C.specifying in advance.

D.specifying in advance.

75.The level of significance is not:

A.the probability of a "false rejection."

B.a value between 0 and 1.

C.the likelihood of rejecting the null hypothesis when it is true.

D.the chance of accepting a true null hypothesis.

76.The critical value in a hypothesis test:

A.is calculated from the sample data.

B.usually is .05 or .01 in most statistical tests.

C.separates the acceptance and rejection regions.

D.depends on the value of the test statistic.

77.Which is not a likely reason to choose the z distribution for a hypothesis test of a mean?

A.The value of is known.

B.The sample size n is very large.

C.The population is normal.

D.The value of is very large.

78.Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. To test DullCo's hypothesis, the test statistic is:

A.-1.980

B.-1.728

C.-2.101

D.-1.960

79.Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. In a left-tailed test at = .05, which is the most accurate statement?

A.We would strongly reject the claim.

B.We would clearly fail to reject the claim.

C.We would face a rather close decision.

D.We would switch to = .01 for a more powerful test.

80.Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. To test DullCo's hypothesis, the p-value is:

A.slightly less than .05.

B.exactly equal to .05.

C.slightly greater than .05.

D.uncertain without knowing .

81.For tests of a mean, if other factors are held constant, which statement is correct?

A.The critical value of Student's t increases as n increases.

B.A test statistic tcalc = 1.853 with n = 16 leads to rejection at = .01 in a one-tailed test.

C.It is harder to reject the null hypothesis in a two-tailed test rather than a one-tailed test.

D.If we desire = .10, then a p-value of .13 would lead us to reject the null hypothesis.

82.For a sample size of n = 100, and = 10, we want to test the hypothesis H0: = 100. The sample mean is 103. The test statistic is:

A.1.645

B.1.960

C.3.000

D.0.300

83.When testing the hypothesis H0: = 100 with n = 100 and 2 = 100, we find that the sample mean is 97. The test statistic is:

A.-3.000

B.-10.00

C.-0.300

D.-0.030

84.Given a normal distribution with = 3, we want to test the hypothesis H0: = 20. We find that the sample mean is 21. The test statistic is:

A.1.000

B.1.645

C.1.960

D.impossible to find without more information.

85.In testing a proportion, which of the following statements is incorrect?

A.Using = .05 rather than = .01 would make it more likely that H0 will be rejected.

B.When the sample proportion is p = .02 and n = 150, it is safe to assume normality.

C.An 80 percent confidence interval is narrower than the 90 percent confidence interval, ceteris paribus.

D.The sample proportion may be assumed approximately normal if the sample is large enough.

86.Which of the following is not a characteristic of the t distribution?

A.It is a continuous distribution.

B.It has a mean of zero.

C.It a symmetric distribution.

D.It is similar to the z distribution when n is small.

87.Which of the following is not a valid null hypothesis?

A.H0: 0

B.H0: 0

C.H0: 0

D.H0: = 0

88.Given that in a one-tail test you cannot reject H0, can you reject H0 in a two-tailed test at the same ?

A.Yes.

B.No.

C.Maybe.

89.The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm. Which are the hypotheses to test whether the mean is smaller than it is supposed to be?

A.H0: 56, H1: > 56

B.H0: 56, H1: < 56

C.H0: = 56, H1: 56

D.H0: < 56, H1: 56

90.The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm. Find the test statistic to see whether the candy bars are smaller than they are supposed to be.

A.-1.636

B.-1.645

C.-1.677

91.The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm. Find the p-value for a test to see whether the candy bars are smaller than they are supposed to be.

A.Between .05 and .10

B.Between .025 and .05

C.Between .01 and .025

D.Less than .01

92.A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. Find the test statistic to decide whether the mean transaction time exceeds 60 seconds.

A.1.457

B.2.037

C.2.333

D.1.848

93.A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. State the hypotheses to test whether the mean transaction time exceeds 60 seconds.

A.H0: 60, H1: > 60

B.H0: 60, H1: < 60

C.H0: = 60, H1: 60

D.H0: < 60, H1: 60

94.A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. Find the critical value to test whether the mean transaction time exceeds 60 seconds at = .01.

A.2.947

B.2.602

C.2.583

D.2.333

95.Given H0: 18 and H1: < 18, we would commit Type I error if we:

A.conclude that 18 when the truth is that < 18.

B.conclude that < 18 when the truth is that 18.

C.fail to reject 18 when the truth is that < 18.

96.For a right-tailed test of a hypothesis for a single population mean with n = 10, the value of the test statistic was t = 1.411. The p-value is:



C.greater than .10.

D.less than .001.

97.Last year, 10 percent of all teenagers purchased a new iPhone. This year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iPhone. The test statistic to find out whether the percent has risen would be:

A.2.687

B.2.758

C..0256

D.2.258

98.Last year, 10 percent of all teenagers purchased a new iPhone. This year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iPhone. To test whether the percent has risen, the critical value at = .05 is:

A.1.645

B.1.658

C.1.697

D.1.960

99.Last year, 10 percent of all teenagers purchased a new iPhone. This year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iPhone. To test whether the percent has risen, the p-value is approximately:

A..0501

B..0314

C..0492

D..0036

100.Ajax Peanut Butter's quality control allows 2 percent of the jars to exceed the quality standard for insect fragments. A sample of 150 jars from the current day's production reveals that 30 exceed the quality standard for insect fragments. Which is incorrect?

A.Normality of p may safely be assumed in the hypothesis test.

B.A right-tailed test would be appropriate.

C.Common sense suggests that quality control standards aren't met.

D.Type II error is more of a concern in this case than Type I error.

101.In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is:

A.-1.645

B.-2.066

C.-2.000

D.-1.960

102.The hypotheses H0: .40, H1: < .40 would require:

A.a left-tailed test.

B.a right-tailed test.

C.a two-tailed test.

103.At = .05, the critical value to test the hypotheses H0: .40, H1: < .40 would be:

A.- 1.645

B.- 1.960

C.- 2.326

D.impossible to determine without more information.

104.In a test of a mean, the reported p-value is .025. Using =.05 the conclusion would be to:

A.accept the null hypothesis.

B.reject the null hypothesis.

C.fail to reject the null hypothesis.

D.gather more evidence due to inconclusive results.

105.Which of the following decisions could result in a Type II error for a test?

A.Reject the alternative hypothesis

B.Reject the null hypothesis

C.Fail to reject the null hypothesis

D.Make no decision

106.The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it. A trial sample of 25 employees shows that 16 are dissatisfied. In this problem:

A.normality of the sample proportion should not be assumed.

B.normality of the sample proportion can be assumed.

C.normality of the sample proportion cannot be judged without knowing .

107.The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it. A trial sample of 25 employees shows that 16 are dissatisfied. The p-value for a right-tailed test is:

A..1337

B..4192

C..0901

D..0808

108.The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it. A trial sample of 25 employees shows that 16 are dissatisfied. For a right-tailed test, the test statistic would be:

A.1.227

B.1.375

C.1.400

D.1.115

109.If sample size increases from 25 to 100 and the level of significance stays the same, then:

A.the risk of Type II error would decrease.

B.the risk of Type I error would decrease.

C.the risk of both Type I and Type II errors would decrease.

D.the risk of neither Type I nor Type II error would decrease.

110."Currently, only 20 percent of arrested drug pushers are convicted," cried candidate Courageous Calvin in a campaign speech. "Elect me and you'll see a big increase in convictions." A year after his election a random sample of 144 case files of arrested drug pushers showed 36 convictions. For a right-tailed test, the p-value is approximately:

A.0.9332

B.0.0668

C.0.0435

D.0.0250

111.In a right-tailed test, a statistician got a z test statistic of 1.47. What is the p-value?

A..4292

B..0709

C..0874

D..9292

112.In a left-tailed test, a statistician got a z test statistic of -1.720. What is the p-value?

A..4292

B..0709

C..0427

D..0301

113.In a two-tailed test, a statistician got a z test statistic of 1.47. What is the p-value?

A..0708

B..1416

C..0874

D..0301

114.Which of the following statements is true?

A.Decreasing will increase the power of the test.

B.Doubling the sample size will double the power of the test.

C.A higher standard deviation would increase the power if we are testing a mean.

D.Power of the test rises if the true mean is farther from the hypothesized mean.

115.High power in a hypothesis test about one sample mean is likely to be associated with:

A.small sample size.

B.low .

C.large .

D.small .

116.The power of a test is the probability of:

A.concluding H1 when H1 is true.

B.concluding H1 when H0 is true.

C.concluding H0 when H0 is true.

D.concluding H0 when H1 is true.

117.Which is not a step in hypothesis testing?

A.Formulate the hypotheses.

B.Specify the desired Type I error.

C.Find the test statistic from a table.

D.Formulate a decision rule.

118.Which is an invalid alternative hypothesis?

A.H1: 18

B.H1: = 18

C.H1: > 18

D.H1: < 18

119.Which is a valid null hypothesis?

A.H0: 18

B.H0: = 18

C.H0: > 18

D.H0: < 18

120.A two-tailed hypothesis test for H0: = .30 at = .05 is analogous to

A.asking if the 90 percent confidence interval for contains .30.

B.asking if the 95 percent confidence interval for contains .30.

C.asking if the p-value (area in both tails combined) is less than .025.

D.asking if the p-value (area in both tails combined) is less than .10.

121.For a right-tailed test of hypothesis for a population mean with known , the test statistic was z = 1.79. The p-value is:

A..0367

B..9633

C..1186

D..0179

122.If n = 25 and = .05 in a right-tailed test of a mean with unknown , the critical value is:

A.1.960

B.1.645

C.1.711

D..0179

123.The researcher's null hypothesis is H0: 2 22. A sample of n = 25 items yields a sample variance of s2 = 28.5. The critical value of chi-square for a right-tailed test at = 05 is:

A.1.960

B.1.645

C.13.85

D.36.42

124.The researcher's null hypotheses is H0: 2 22. A sample of n = 25 items yields a sample variance of s2 = 28.5. The test statistic is:

A.31.09.

B.26.42.

C.must know if it is a one-tailed test.

D.must know to answer.

125.The researcher's null hypothesis is H0: 2 = 420. A sample of n = 18 items yields a sample variance of s2 = 512. The critical values of chi-square for a two-tailed test at = .05 are:

A.8.672 and 27.59

B.7.564 and 30.19

C.-1.960 and +1.960

D.9.390 and 28.87

126.The researcher's null hypotheses is H0: 2 = 420. A sample of n = 18 items yields a sample variance of s2 = 512. The test statistic is:

A.34.09

B.20.72

C.14.77

D.must know to answer.

127.In hypothesis testing, Type I error is:

A.always set at 5 percent.

B.smaller than or equal to 5 percent.

C.the probability of rejecting H0 when H0 is true.

D.the probability of rejecting H0 when H1 is true.

128.In hypothesis testing, the value of is:

A.equal to 1 minus the probability of committing Type I error.

B.the probability of concluding H0 when H0 is true.

C.the probability of concluding H0 when H1 is true.

129.Regarding the probability of Type I error () and Type II error (), which statement is true?

A. >

B. <

C. + = 1

D.Power = 1 - .

130.In the hypothesis H0: = 0, the value of 0 is not derived from:

A.the sample.

B.past experience.

C.a target or benchmark.

D.a scientific theory.

131.In testing the hypotheses H0: 0, H1: > 0, we would use a:

A.two-tailed test.

B.left-tailed test.

C.right-tailed test.

D.breathalyzer test.

132.We can assume that the sample proportion is normally distributed if:

A.we have 10 successes in the sample.

B.we have 10 failures in the sample.

C.we have both 10 successes and 10 failures in the sample.

D.the population is known.

Short Answer Questions133.Julia hypothesizes that fewer than 90 percent of her Visa purchases are under $100. She examines a random sample of her recent purchases and performs a test. The results shown below are from MegaStat. What would Julia conclude from this test? Explain carefully.

134.Why is it better to say "fail to reject H0" instead of "accept H0"?

135.Mary examined a random sample of Friday withdrawals from a college campus ATM. She hypothesized that the mean was less than $100. The results shown below are from MegaStat. What would Mary conclude from this test? Explain carefully.

136.Bob hypothesizes that the average student at his university has to take more than 130 credits to graduate. He takes a random sample of his classmates and performs a test. The results shown below are from MegaStat. What would Bob conclude from this test? Explain carefully.

137.Pedro hypothesizes that more than half of his classmates would prefer a virtual web graduation ceremony, rather than sitting in the hot sun during the commencement speech. He takes a random sample of his classmates and performs a test. The results shown below are from MegaStat. What would Pedro conclude from this test? Explain carefully.

Chapter 09 One-Sample Hypothesis Tests Answer Key

True / False Questions1.The level of significance refers to the probability of making a Type II error.FALSEThe level of significance is the desired probability of Type I error.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 09-03 Define Type I error; Type II error; and power.Topic: Logic of Hypothesis Testing

2.The level of significance refers to the probability of making a Type I error.TRUEThe level of significance is the desired probability of Type I error.


3.A simultaneous reduction in both and will require a larger sample size.TRUEIn general, there is a trade-off between and , but with a larger n we can reduce both.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 09-03 Define Type I error; Type II error; and power.Topic: Logic of Hypothesis Testing

4.The probability of rejecting a false null hypothesis increases as the sample size increases, other things being equal.TRUELarger samples cut the chance of Type II error () and increase power (1 - ).


5.When the probability of a Type I error increases, the probability of a Type II error must decrease, ceteris paribus.TRUEFor a given sample size, there is a trade-off between and .


6.A false positive in a drug test for steroids is a Type II error.FALSEA false positive is a Type I error.


7.If a judge acquits every defendant, the judge will never commit a Type I error (H0 is the hypothesis of innocence).TRUEIf no one is convicted, there is no Type I error (but there can be Type II error).


8.When your sample size increases, the chance of both Type I and Type II error will increase.FALSEThere is a trade-off between and unless we can increase n.


9.A Type II error can only occur when you fail to reject H0.TRUEIf you don't reject H0, you may commit Type II error.


10.A Type I error can only occur if you reject H0.TRUEIf you reject H0, a false positive can occur.


11.John rejected H0 so we know definitely that he did not commit Type II error.TRUEIf you reject H0, you may commit Type I error but not Type II error.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 09-03 Define Type I error; Type II error; and power.Topic: Logic of Hypothesis Testing

12.In hypothesis testing we cannot prove a null hypothesis is true.TRUEThe null hypothesis could be falsified by a different sample.


13.For a given level of significance (), increasing the sample size will increase the probability of Type II error because there are more ways to make an incorrect decision.FALSELarge sample size is beneficial in reducing error of either type.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 09-03 Define Type I error; Type II error; and power.Topic: Statistical Hypothesis Testing

14.For a given sample size, reducing the level of significance will decrease the probability of making a Type II error.FALSEFor fixed n, reducing would tend to increase .

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 09-03 Define Type I error; Type II error; and power.Topic: Statistical Hypothesis Testing

15.The probability of a false positive is decreased if we reduce .TRUEBy definition, is the chance of a false positive.


16.A hypothesis test may be statistically significant, yet have little practical importance.TRUESmall effects may be unimportant in some applications.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 09-06 Perform a hypothesis test for a mean with known using z.Topic: Testing a Mean: Known Population Variance

17.Compared to using = .01, choosing = .001 will make it less likely that a true null hypothesis will be rejected.TRUESmaller makes it harder to reject the null hypothesis (but may increase ).

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 09-08 Use tables or Excel to find the p-value in tests of .Topic: Statistical Hypothesis Testing

18.A two-tailed hypothesis test for H0: = 15 at = .10 is analogous to asking if a 90 percent confidence interval for contains 15.TRUEOnly in a two-tailed hypothesis test is this statement true.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 09-06 Perform a hypothesis test for a mean with known using z.Topic: Testing a Mean: Known Population Variance

19.For a given sample size and level, the Student's t value always exceeds the z value.TRUEAs n increases, t approaches z, but t is always larger.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 09-07 Perform a hypothesis test for a mean with unknown using t.Topic: Testing a Mean: Unknown Population Variance

20.For a given level of significance, the critical value of Student's t increases as n increases.FALSEAs n increases, t declines and approaches the corresponding z.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 09-07 Perform a hypothesis test for a mean with unknown using t.Topic: Testing a Mean: Unknown Population Variance

21.For a sample of nine items, the critical value of Student's t for a left-tailed test of a mean at = .05 is -1.860.TRUEUse Appendix D or Excel's function =T.INV(.05,8).

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 09-05 Find critical values of z or t in tables or by using Excel.Topic: Testing a Mean: Unknown Population Variance

22.Holding other factors constant, it is harder to reject the null hypothesis for a mean when conducting a two-tailed test rather than a one-tailed test.TRUEFor a two-tailed test, the critical value is farther out in the tail.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 09-03 Define Type I error; Type II error; and power.Topic: Testing a Mean: Known Population Variance

23.If we desire = .10, then a p-value of .13 would lead us to reject the null hypothesis.FALSEReject the null if the p-value is less than .

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 09-08 Use tables or Excel to find the p-value in tests of .Topic: Testing a Mean: Known Population Variance

24.The p-value is the probability of the sample result (or one more extreme) assuming H0 is true.TRUEThis is the definition of a p-value.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 09-08 Use tables or Excel to find the p-value in tests of .Topic: Testing a Mean: Known Population Variance

25.The probability of rejecting a true null hypothesis is the significance level of the test.TRUEThis is the definition of .

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 09-03 Define Type I error; Type II error; and power.Topic: Logic of Hypothesis Testing

26.A null hypothesis is rejected when the calculated p-value is less than the critical value of the test statistic.FALSENo, the p-value is compared with (not with the critical value from a table).

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 09-08 Use tables or Excel to find the p-value in tests of .Topic: Testing a Mean: Known Population Variance

27.In a right-tailed test, the null hypothesis is rejected when the value of the test statistic exceeds the critical value.TRUEFor example, we would reject H0 if zcalc > 1.645 at = .05.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 09-05 Find critical values of z or t in tables or by using Excel.Topic: Statistical Hypothesis Testing

28.The critical value of a hypothesis test is based on the researcher's selected level of significance.TRUEThe level of significance is the desired tail area, which dictates the critical value.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 09-05 Find critical values of z or t in tables or by using Excel.Topic: Statistical Hypothesis Testing

29.If the null and alternative hypotheses are H0: 100 and H1: > 100, the test is right-tailed.TRUEThe direction of the test is always revealed by the direction of the inequality in H1.

AACSB: AnalyticBlooms: UnderstandDifficulty: 1 EasyLearning Objective: 09-04 Formulate a null and alternative hypothesis for or .Topic: Statistical Hypothesis Testing

30.The null hypothesis is rejected when the p-value exceeds the level of significance.FALSEReject the null if the p-value is less than .

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 09-08 Use tables or Excel to find the p-value in tests of .Topic: Testing a Mean: Known Population Variance

31.For a given null hypothesis and level of significance, the critical value for a two-tailed test is greater than the critical value for a one-tailed test.TRUEFor a two-tailed test, we have to go farther into the tails to put /2 in the tail.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 09-05 Find critical values of z or t in tables or by using Excel.Topic: Statistical Hypothesis Testing

32.For a given Ho and level of significance, if you reject the H0 for a one tailed-test, you would also reject H0 for a two-tailed test.FALSEThe opposite is true because the two-tailed critical value is bigger.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 09-05 Find critical values of z or t in tables or by using Excel.Topic: Statistical Hypothesis Testing

33.If the hypothesized proportion is 0 = .025 in a sample of size 120, it is safe to assume normality of the sample proportion p.FALSEWe can assume normality of p if n0 10 and n(1 - 0) 10, which is not true here.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 09-09 Perform a hypothesis test for a proportion and find the p-value.Topic: Testing a Proportion

34.For a mean, we would expect the test statistic to be near zero if the null hypothesis is true.TRUEThe difference between the sample mean and the hypothesized mean would be small.

AACSB: AnalyticBlooms: UnderstandDifficulty: 1 EasyLearning Objective: 09-06 Perform a hypothesis test for a mean with known using z.Topic: Testing a Mean: Known Population Variance

35.In the hypothesis H0: = 0, the value of 0 is derived from the sample.FALSEThe hypothesized proportion is a target or historical benchmark.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 09-09 Perform a hypothesis test for a proportion and find the p-value.Topic: Testing a Proportion

36.In testing the hypotheses H0: 0, H1: > 0, we would use a right-tailed test.TRUEThe direction of the test is always revealed by the direction of the inequality in H1.


37.To test the hypothesis H0: = .0125 using n = 160, it is safe to assume normality of p.FALSEWe can assume normality of p if n0 10 and n(1 - 0) 10, which is not true here.


38.In testing a proportion, normality of p can be assumed if n0 10 and n(1 - 0) 10.TRUEThis is a conservative rule of thumb.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 09-09 Perform a hypothesis test for a proportion and find the p-value.Topic: Testing a Proportion

39.Power is the probability of rejecting the null hypothesis when it is false and is equal to 1 - .TRUEHigh power (small chance of Type II error) is desirable.


40.Other things being equal, a smaller standard deviation implies higher power.TRUEHigher variance makes it harder to detect a departure from H0.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 09-10 Interpret a power curve or OC curve (optional).Topic: Power Curves and OC Curves (Optional)

41.The power of a test is the probability that the test will reject a false null hypothesis.TRUEHigh power (small chance of Type II error) is desirable.


42.The height of the power curve shows the probability of accepting a true null hypothesis.FALSEPower is the chance of correctly rejecting a false null hypothesis.

AACSB: AnalyticBlooms: UnderstandDifficulty: 3 HardLearning Objective: 09-10 Interpret a power curve or OC curve (optional).Topic: Power Curves and OC Curves (Optional)

43.The power curve plots on the Y axis and the test statistic on the X axis.FALSEA power curve plots the true parameter value on the X-axis and 1 - on the Y-axis.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 09-10 Interpret a power curve or OC curve (optional).Topic: Power Curves and OC Curves (Optional)

44.A smaller probability of Type II error implies higher power of the test.TRUEBy definition, power is 1 - .


45.Varying the true mean is a movement along the power curve, not a shift in the curve.TRUEThe power curve shows how power varies with the true mean.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 09-10 Interpret a power curve or OC curve (optional).Topic: Power Curves and OC Curves (Optional)

46.Increasing the sample size shifts the power curve upward, ceteris paribus.TRUELarger n would raise the power curve at all points along the X-axis.


47.Increasing the level of significance shifts the power curve upward, ceteris paribus.TRUEFor a given n, increasing would decrease and hence raise power (1 - ).


48.A power curve for a mean is at its lowest point when the true is very near 0.TRUEThis is why it is hard to detect small departures from H0.


49.Larger samples lead to increased power, ceteris paribus.TRUELarger n would raise the power curve at all points along the X-axis.


50.In graphing power curves, there is a different power curve for each sample size n.TRUELarger n would raise the power curve at all points along the X-axis.


51.In hypothesis testing, we are trying to reject the alternative hypothesis.FALSEWe are trying to reject the null hypothesis H0.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 09-02 Explain the difference between H0 and H1.Topic: Logic of Hypothesis Testing

52.In hypothesis testing, we are trying to prove the null hypothesis.FALSEWe cannot prove the null hypothesis, for H0 could be falsified by a different sample.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 09-02 Explain the difference between H0 and H1.Topic: Logic of Hypothesis Testing

53.When is unknown, it is more conservative to use z instead of t for the critical value.FALSEBecause z is smaller than t we would reject too often if we use z (not conservative).

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 09-07 Perform a hypothesis test for a mean with unknown using t.Topic: Testing a Mean: Unknown Population Variance

Multiple Choice Questions54.For a given sample size, when we increase the probability of Type I error, the probability of a Type II error:

A.remains unchanged.

B.increases.

C.decreases.

D.is impossible to determine without more information.

For a given sample size, there is a trade-off between and .


55.After testing a hypothesis regarding the mean, we decided not to reject H0. Thus, we are exposed to:

A.Type I error.

B.Type II error.



Failure to reject H0 could lead to Type II error (but not Type I error).


56.After testing a hypothesis, we decided to reject the null hypothesis. Thus, we are exposed to:

A.Type I error.

B.Type II error.



Rejecting H0 could lead to Type I error (but not Type II error).


57.Which statement about is not correct?

A.It is the probability of committing a Type I error.

B.It is the test's significance level.

C.It is the probability of rejecting a true H0.

D.It is equal to 1 - .

There is an inverse relationship between and , but it is not a simple equation.


58.Which of the following is correct?

A.When sample size increases, both and may decrease.

B.Type II error can only occur when you reject H0.

C.Type I error can only occur if you fail to reject H0.

D.The level of significance is the probability of Type II error.

Only a larger sample can allow a reduction in both and (ceteris paribus).


59.Which of the following is incorrect?

A.The level of significance is the probability of making a Type I error.

B.Lowering both and at once will require a higher sample size.

C.The probability of rejecting a true null hypothesis increases as n increases.

D.When Type I error increases, Type II error must decrease, ceteris paribus.

The critical value for the desired takes the sample size into consideration.


60.John rejected his null hypothesis in a right-tailed test for a mean at = .025 because his critical t value was 2.000 and his calculated t value was 2.345. We can be sure that:

A.John did not commit Type I error.

B.John did not commit Type II error.

C.John committed neither Type I nor Type II error.

D.John committed both Type I and Type II error.

John could have committed Type II error only if he failed to reject H0.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 09-03 Define Type I error; Type II error; and power.Topic: Logic of Hypothesis Testing

61."My careful physical examination shows no evidence of any serious problem," said Doctor Morpheus. "However, a very costly lab test can be performed to check for the rare condition known as estomalgia fatalis. The test is almost invariably negative for persons with your age and symptoms. My personal hypothesis is that the occasional stomach pain you reported is due to indigestion caused by eating tacos with too much hot sauce. But you must decide for yourself." As you consider your doctor's hypothesis, what would be the consequence of Type I error on your part?

A.It can't be determined without knowing the type of test.

B.Your estomalgia fatalis will go undetected.

C.You will waste money on an unnecessary lab test.

D.Your survivors will enjoy a sizeable malpractice award.

Type I error is rejecting the doctor's advice when it was correct.


62.Which of the following statements is correct?

A.Increasing will make it more likely that we will reject H0, ceteris paribus.

B.Doubling the sample size roughly doubles the test statistic, ceteris paribus.

C.A higher standard deviation would increase the power of a test for a mean.

D.The p-value shows the probability that the null hypothesis is false.

A larger will make it easier to reject H0 (e.g., z.05 = 1.645 versus z.01 = 2.326).


63."I believe your airplane's engine is sound," states the mechanic. "I've been over it carefully, and can't see anything wrong. I'd be happy to tear the engine down completely for an internal inspection at a cost of $1,500. But I believe that engine roughness you heard in the engine on your last flight was probably just a bit of water in the fuel, which passed harmlessly through the engine and is now gone." As the pilot considers the mechanic's hypothesis, the cost of Type I error is:

A.the pilot will experience the thrill of no-engine flight.

B.the pilot will be out $1,500 unnecessarily.

C.the mechanic will lose a good customer.

D.impossible to determine without knowing .

Type I error is rejecting the mechanic's advice when it was correct.


64.A study over a 10-year period showed that a certain mammogram test had a 50 percent rate of false positives. This indicates that:

A.about half the tests indicated cancer.

B.about half the tests missed a cancer that exists.

C.about half the tests showed a cancer that didn't exist.

D.about half the women tested actually had no cancer.

This is a 50 percent chance of Type I error.


65.You are driving a van packed with camping gear (total weight 3,500 pounds including yourself and family) into a northern wilderness area. You take a "short cut" that turns into a one-lane road, with no room to turn around. After 11 miles you come to a narrow bridge with a faded sign saying "Safe Up to 2 Tons." About a half-mile ahead, you can see that your road rejoins the main highway. You consider the sign's hypothesis carefully before making a decision. The cost of Type I error is:

A.you pass safely over the bridge and everyone's happy.

B.about $23,900, not including medical bills.

C.you will find out just how cold that river actually is.

D.your kids will think you're a chicken.

Type I error is rejecting the sign's message when it was correct.


66.After lowering the landing gear, the pilot notices that the "gear down and locked" light is not illuminated. "It's probably just a burned out light bulb," she says, as she proceeds on final approach for landing. Considering the pilot's hypothesis, which is the result of Type I error?

A.The sound of metal scraping on concrete will be heard upon landing.

B.The landing is delayed unnecessarily while the bulb and gear are checked.

C.We cannot be sure without knowing whether or not the bulb is actually faulty.

Type I error is concluding there is a problem when there was not.


67.As you are crossing a field at the farm, your country cousin Jake assures you, "Don't worry about that old bull coming toward us. He's harmless." As you consider Jake's hypothesis, what would be Type I error on your part?

A.You will soon feel the bull's horns.

B.You will run away for no good reason.

C.Jake will not have any more visits from you.

Type I error is rejecting Jake's advice when he was right.


68.Which is not true of p-values?

A.When they are small, we want to reject H0.

B.They measure the probability of an incorrect decision.

C.They show the chance of Type I error if we reject H0.

D.They do not require to be specified a priori.

The p-value tells the likelihood of the sample assuming that H0 is true.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 09-08 Use tables or Excel to find the p-value in tests of .Topic: Testing a Mean: Known Population Variance

69.For a test of a mean, which of the following is incorrect?

A.H0 is rejected when the calculated p-value is less than the critical value of the test statistic.

B.In a right-tailed test, we reject H0 when the test statistic exceeds the critical value.

C.The critical value is based on the researcher's chosen level of significance.

D.If H0: 100 and H1: > 100, then the test is right-tailed.

We compare the p-value with (not with the critical value).

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 09-08 Use tables or Excel to find the p-value in tests of .Topic: Testing a Mean: Known Population Variance

70.Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours. A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital and found a mean hospital stay of 40 hours with a standard deviation of 20 hours. "Aha!" she cried, "the average stay exceeds the guideline." At = .025, the critical value for a right-tailed test of her hypothesis is:

A.1.753

B.2.131

C.1.645

D.1.960

Using Appendix D with d.f. = 16 - 1 = 15, we get t.025 = 2.131.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 09-05 Find critical values of z or t in tables or by using Excel.Topic: Testing a Mean: Unknown Population Variance

71.Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours. A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital and found a mean hospital stay of 40 hours with a standard deviation of 20 hours. "Aha!" she cried, "the average stay exceeds the guideline." The value of the test statistic for her hypothesis is:

A.2.080

B.0.481

C.1.866

D.2.000

tcalc = (40 - 30)/[(20)/161/2] = 2.000.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 09-07 Perform a hypothesis test for a mean with unknown using t.Topic: Testing a Mean: Unknown Population Variance

72.Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours. A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital, and found a mean hospital stay of 40 hours with a standard deviation of 20 hours. "Aha!" she cried, "the average stay exceeds the guideline." The p-value for a right-tailed test of her hypothesis is:



C.between .01 and .025.

D.less than .01.

Use Appendix D with tcalc = 2.000 or Excel =T.DIST.RT(2.000,15) = .0320.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 09-08 Use tables or Excel to find the p-value in tests of .Topic: Testing a Mean: Unknown Population Variance

73.For a right-tailed test of a hypothesis for a population mean with n = 14, the value of the test statistic was t = 1.863. The p-value is:



C.greater than .10.

D.less than .01.

For d.f. = 13, t.025 = 2.160 and t.05 = 1.771 or Excel =T.DIST.RT(1.863,13) = .0426.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 09-08 Use tables or Excel to find the p-value in tests of .Topic: Testing a Mean: Unknown Population Variance

74.Hypothesis tests for a mean using the critical value method require:

A.knowing the true value of .

B.sampling a normal population.

C.specifying in advance.

D.specifying in advance.

You cannot find the critical value without specifying .

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 09-05 Find critical values of z or t in tables or by using Excel.Topic: Testing a Mean: Known Population Variance

75.The level of significance is not:

A.the probability of a "false rejection."

B.a value between 0 and 1.

C.the likelihood of rejecting the null hypothesis when it is true.

D.the chance of accepting a true null hypothesis.

The level of significance is the risk of rejecting a true null hypothesis.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 09-03 Define Type I error; Type II error; and power.Topic: Statistical Hypothesis Testing

76.The critical value in a hypothesis test:

A.is calculated from the sample data.

B.usually is .05 or .01 in most statistical tests.

C.separates the acceptance and rejection regions.

D.depends on the value of the test statistic.

We can specify whatever we wish to set the desired tail area(s).

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 09-05 Find critical values of z or t in tables or by using Excel.Topic: Statistical Hypothesis Testing

77.Which is not a likely reason to choose the z distribution for a hypothesis test of a mean?

A.The value of is known.

B.The sample size n is very large.

C.The population is normal.

D.The value of is very large.

We use z any time is known.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 09-06 Perform a hypothesis test for a mean with known using z.Topic: Testing a Mean: Known Population Variance

78.Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. To test DullCo's hypothesis, the test statistic is:

A.-1.980

B.-1.728

C.-2.101

D.-1.960

tcalc = (37.8 - 40)/[(5.4)/181/2] = -1.72848.


79.Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. In a left-tailed test at = .05, which is the most accurate statement?

A.We would strongly reject the claim.

B.We would clearly fail to reject the claim.

C.We would face a rather close decision.

D.We would switch to = .01 for a more powerful test.

tcalc = (37.8 - 40)/[(5.4)/181/2] = -1.728, while for d.f. = 18 - 1 = 17 we get t.05 = -1.740, so it is a close decision.


80.Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. To test DullCo's hypothesis, the p-value is:

A.slightly less than .05.

B.exactly equal to .05.

C.slightly greater than .05.

D.uncertain without knowing .

tcalc = -1.728, t.05 = -1.740 or Excel =T.DIST(-1.72848,17,1) = .0511.


81.For tests of a mean, if other factors are held constant, which statement is correct?

A.The critical value of Student's t increases as n increases.

B.A test statistic tcalc = 1.853 with n = 16 leads to rejection at = .01 in a one-tailed test.

C.It is harder to reject the null hypothesis in a two-tailed test rather than a one-tailed test.

D.If we desire = .10, then a p-value of .13 would lead us to reject the null hypothesis.

Rejection in a two-tailed test implies rejection in a one-tailed test, but not vice versa.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 09-07 Perform a hypothesis test for a mean with unknown using t.Topic: Testing a Mean: Unknown Population Variance

82.For a sample size of n = 100, and = 10, we want to test the hypothesis H0: = 100. The sample mean is 103. The test statistic is:

A.1.645

B.1.960

C.3.000

D.0.300

zcalc = (103 - 100)/[(10)/1001/2] = 3.000.


83.When testing the hypothesis H0: = 100 with n = 100 and 2 = 100, we find that the sample mean is 97. The test statistic is:

A.-3.000

B.-10.00

C.-0.300

D.-0.030

zcalc = (97 - 100)/[(10)/1001/2] = -3.000.


84.Given a normal distribution with = 3, we want to test the hypothesis H0: = 20. We find that the sample mean is 21. The test statistic is:

A.1.000

B.1.645

C.1.960

D.impossible to find without more information.

The sample size is needed to calculate the z test statistic.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 09-06 Perform a hypothesis test for a mean with known using z.Topic: Testing a Mean: Known Population Variance

85.In testing a proportion, which of the following statements is incorrect?

A.Using = .05 rather than = .01 would make it more likely that H0 will be rejected.

B.When the sample proportion is p = .02 and n = 150, it is safe to assume normality.

C.An 80 percent confidence interval is narrower than the 90 percent confidence interval, ceteris paribus.

D.The sample proportion may be assumed approximately normal if the sample is large enough.

We want at least 10 "successes," but np = 3 in this example.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 09-09 Perform a hypothesis test for a proportion and find the p-value.Topic: Testing a Proportion

86.Which of the following is not a characteristic of the t distribution?

A.It is a continuous distribution.

B.It has a mean of zero.

C.It a symmetric distribution.

D.It is similar to the z distribution when n is small.

Student's t resembles z most closely for a large sample size.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 09-07 Perform a hypothesis test for a mean with unknown using t.Topic: Testing a Mean: Unknown Population Variance

87.Which of the following is not a valid null hypothesis?

A.H0: 0

B.H0: 0

C.H0: 0

D.H0: = 0

The null hypothesis cannot contain a two-tailed inequality.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 09-04 Formulate a null and alternative hypothesis for or .Topic: Statistical Hypothesis Testing

88.Given that in a one-tail test you cannot reject H0, can you reject H0 in a two-tailed test at the same ?

A.Yes.

B.No.

C.Maybe.

Rejection in a two-tailed test implies rejection in a one-tailed test, but not vice versa.


89.The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm. Which are the hypotheses to test whether the mean is smaller than it is supposed to be?

A.H0: 56, H1: > 56

B.H0: 56, H1: < 56

C.H0: = 56, H1: 56

D.H0: < 56, H1: 56

We want a left-tailed alternative hypothesis.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 09-04 Formulate a null and alternative hypothesis for or .Topic: Testing a Mean: Known Population Variance

90.The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm. Find the test statistic to see whether the candy bars are smaller than they are supposed to be.

A.-1.636

B.-1.645

C.-1.677

zcalc = (55.82 - 56)/[(0.77)/491/2] = -1.63636.


91.The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm. Find the p-value for a test to see whether the candy bars are smaller than they are supposed to be.

A.Between .05 and .10

B.Between .025 and .05

C.Between .01 and .025

D.Less than .01

zcalc = (55.82 - 56)/[(0.77)/491/2] = -1.63636 and z.05 = -1.645, or find the exact p-value as =NORM.S.DIST(-1.63636,1) = .0509.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 09-08 Use tables or Excel to find the p-value in tests of .Topic: Testing a Mean: Known Population Variance

92.A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. Find the test statistic to decide whether the mean transaction time exceeds 60 seconds.

A.1.457

B.2.037

C.2.333

D.1.848

tcalc = (67 - 60)/[(12)/161/2] = 2.333.


93.A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. State the hypotheses to test whether the mean transaction time exceeds 60 seconds.

A.H0: 60, H1: > 60

B.H0: 60, H1: < 60

C.H0: = 60, H1: 60

D.H0: < 60, H1: 60

We want a right-tailed test in this case.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 09-04 Formulate a null and alternative hypothesis for or .Topic: Testing a Mean: Unknown Population Variance

94.A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. Find the critical value to test whether the mean transaction time exceeds 60 seconds at = .01.

A.2.947

B.2.602

C.2.583

D.2.333

For d.f. = 15, use Appendix D to find t.01 = 2.602.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 09-05 Find critical values of z or t in tables or by using Excel.Topic: Testing a Mean: Unknown Population Variance

95.Given H0: 18 and H1: < 18, we would commit Type I error if we:

A.conclude that 18 when the truth is that < 18.

B.conclude that < 18 when the truth is that 18.

C.fail to reject 18 when the truth is that < 18.

Rejecting a true null hypothesis is Type I error.


96.For a right-tailed test of a hypothesis for a single population mean with n = 10, the value of the test statistic was t = 1.411. The p-value is:



C.greater than .10.

D.less than .001.

From Appendix D with d.f. = 9, t.05 = 1.833 and t.10 = 1.383.


97.Last year, 10 percent of all teenagers purchased a new iPhone. This year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iPhone. The test statistic to find out whether the percent has risen would be:

A.2.687

B.2.758

C..0256

D.2.258

p = 39/260 = .15, 0 = .10, zcalc = (.15 - .10)/[(.10)(1 - .10)/260]1/2 = 2.68742.


98.Last year, 10 percent of all teenagers purchased a new iPhone. This year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iPhone. To test whether the percent has risen, the critical value at = .05 is:

A.1.645

B.1.658

C.1.697

D.1.960

z.05 = 1.645.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 09-05 Find critical values of z or t in tables or by using Excel.Topic: Testing a Proportion

99.Last year, 10 percent of all teenagers purchased a new iPhone. This year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iPhone. To test whether the percent has risen, the p-value is approximately:

A..0501

B..0314

C..0492

D..0036

p = 39/260 = .15, 0 = .10, zcalc = (.15 - .10)/[(.10)(1 - .10)/260]1/2 = 2.68742, so from Appendix C we get P(Z > 2.69) = .0036 or from Excel =1-NORM.S.DIST(2.68742,1) = .0036.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 09-09 Perform a hypothesis test for a proportion and find the p-value.Topic: Testing a Proportion

100.Ajax Peanut Butter's quality control allows 2 percent of the jars to exceed the quality standard for insect fragments. A sample of 150 jars from the current day's production reveals that 30 exceed the quality standard for insect fragments. Which is incorrect?

A.Normality of p may safely be assumed in the hypothesis test.

B.A right-tailed test would be appropriate.

C.Common sense suggests that quality control standards aren't met.

D.Type II error is more of a concern in this case than Type I error.

n0 = (150)(.02) = 3, so normality of p is doubtful.


101.In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is:

A.-1.645

B.-2.066

C.-2.000

D.-1.960

p = 24/64 = .375, 0 = .50, zcalc = (.375 - .50)/[(.50)(1 - .50)/64]1/2 = - 2.000.


102.The hypotheses H0: .40, H1: < .40 would require:

A.a left-tailed test.

B.a right-tailed test.

C.a two-tailed test.

The inequality in the alternative hypothesis points to the direction of the test.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 09-04 Formulate a null and alternative hypothesis for or .Topic: Testing a Proportion

103.At = .05, the critical value to test the hypotheses H0: .40, H1: < .40 would be:

A.- 1.645

B.- 1.960

C.- 2.326

D.impossible to determine without more information.

z.05 = - 1.645.


104.In a test of a mean, the reported p-value is .025. Using =.05 the conclusion would be to:

A.accept the null hypothesis.

B.reject the null hypothesis.

C.fail to reject the null hypothesis.

D.gather more evidence due to inconclusive results.

Reject the null hypothesis if the p-value is smaller than .


105.Which of the following decisions could result in a Type II error for a test?

A.Reject the alternative hypothesis

B.Reject the null hypothesis

C.Fail to reject the null hypothesis

D.Make no decision

Failing to reject H0 could lead to Type II error (but not Type I error).

AACSB: AnalyticBlooms: UnderstandDifficulty: 1 EasyLearning Objective: 09-03 Define Type I error; Type II error; and power.Topic: Logic of Hypothesis Testing

106.The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it. A trial sample of 25 employees shows that 16 are dissatisfied. In this problem:

A.normality of the sample proportion should not be assumed.

B.normality of the sample proportion can be assumed.

C.normality of the sample proportion cannot be judged without knowing .

n0 = (25)(.50) = 12.5, so we expect at least 10 "successes" and 10 "failures" (be careful to use 0 instead of p to check for normality).


107.The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it. A trial sample of 25 employees shows that 16 are dissatisfied. The p-value for a right-tailed test is:

A..1337

B..4192

C..0901

D..0808



108.The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it. A trial sample of 25 employees shows that 16 are dissatisfied. For a right-tailed test, the test statistic would be:

A.1.227

B.1.375

C.1.400

D.1.115

p = 16/25 = .64, 0 = .50, zcalc = (.64 - .50)/[(.50)(1 - .50)/25]1/2 = 1.400.


109.If sample size increases from 25 to 100 and the level of significance stays the same, then:

A.the risk of Type II error would decrease.

B.the risk of Type I error would decrease.

C.the risk of both Type I and Type II errors would decrease.

D.the risk of neither Type I nor Type II error would decrease.

We are holding constant so the larger sample will reduce .


110."Currently, only 20 percent of arrested drug pushers are convicted," cried candidate Courageous Calvin in a campaign speech. "Elect me and you'll see a big increase in convictions." A year after his election a random sample of 144 case files of arrested drug pushers showed 36 convictions. For a right-tailed test, the p-value is approximately:

A.0.9332

B.0.0668

C.0.0435

D.0.0250



111.In a right-tailed test, a statistician got a z test statistic of 1.47. What is the p-value?

A..4292

B..0709

C..0874

D..9292

From Appendix C we get P(Z > 1.47) = .0708 or from Excel =1-NORM.S.DIST(1.47,1) = .0708.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 09-08 Use tables or Excel to find the p-value in tests of .Topic: Testing a Proportion

112.In a left-tailed test, a statistician got a z test statistic of -1.720. What is the p-value?

A..4292

B..0709

C..0427

D..0301

From Appendix C we get P(Z < -1.72) = .0427 or from the Excel function =NORM.S.DIST(-1.720,1) = .0427.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 09-08 Use tables or Excel to find the p-value in tests of .Topic: Testing a Proportion

113.In a two-tailed test, a statistician got a z test statistic of 1.47. What is the p-value?

A..0708

B..1416

C..0874

D..0301

From Appendix C we get 2 P(Z > 1.47) = 2 .0708 = .1416. The Excel version of this calculation is =2*(1-NORM.S.DIST(1.47,1)) = 0.14156.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 09-08 Use tables or Excel to find the p-value in tests of .Topic: Testing a Mean: Known Population Variance

114.Which of the following statements is true?

A.Decreasing will increase the power of the test.

B.Doubling the sample size will double the power of the test.

C.A higher standard deviation would increase the power if we are testing a mean.

D.Power of the test rises if the true mean is farther from the hypothesized mean.

A test becomes more sensitive (greater power) when the truth differs greatly from H0.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 09-10 Interpret a power curve or OC curve (optional).Topic: Power Curves and OC Curves (Optional)

115.High power in a hypothesis test about one sample mean is likely to be associated with:

A.small sample size.

B.low .

C.large .

D.small .

Less variation in the population makes the test more sensitive (greater power).


116.The power of a test is the probability of:

A.concluding H1 when H1 is true.

B.concluding H1 when H0 is true.

C.concluding H0 when H0 is true.

D.concluding H0 when H1 is true.

Review the definition of power.


117.Which is not a step in hypothesis testing?

A.Formulate the hypotheses.

B.Specify the desired Type I error.

C.Find the test statistic from a table.

D.Formulate a decision rule.

Review the steps in hypothesis testing.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 09-01 List the steps in testing hypotheses.Topic: Logic of Hypothesis Testing

118.Which is an invalid alternative hypothesis?

A.H1: 18

B.H1: = 18

C.H1: > 18

D.H1: < 18

You cannot have an equality in the alternative hypothesis.


119.Which is a valid null hypothesis?

A.H0: 18

B.H0: = 18

C.H0: > 18

D.H0: < 18

The null hypothesis cannot have < or > or .


120.A two-tailed hypothesis test for H0: = .30 at = .05 is analogous to

A.asking if the 90 percent confidence interval for contains .30.

B.asking if the 95 percent confidence interval for contains .30.

C.asking if the p-value (area in both tails combined) is less than .025.

D.asking if the p-value (area in both tails combined) is less than .10.

This statement is true for a two-tailed test only.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 09-09 Perform a hypothesis test for a proportion and find the p-value.Topic: Testing a Proportion

121.For a right-tailed test of hypothesis for a population mean with known , the test statistic was z = 1.79. The p-value is:

A..0367

B..9633

C..1186

D..0179

From Appendix C we get P(Z > 1.79) = .0367 or from Excel =1-NORM.S.DIST(1.79,1) = .0367.


122.If n = 25 and = .05 in a right-tailed test of a mean with unknown , the critical value is:

A.1.960

B.

chap 009

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