The Quiz Show

To review and help prepare you for the final exam...

How we’ll play …

• Break up into groups of up to 4 people.

• Complete one answer sheet per group.

• I’ll show you questions -- each question only for a certain amount of time

• Your group should work together to determine the answer. No notes, books, or calculators permitted.

How we’ll play … (continued)

• One group member writes down the group’s answer on the sheet.

• When we discuss the answers, each group must volunteer at least one of their answers.

Two sample T for height

gender N Mean StDev SE MeanM 84 70.05 3.03 0.33F 89 64.80 2.88 0.30

95% CI for mu (M) - mu (F): ( 4.36, 6.14)T-Test mu (M) = mu (F) (vs >): T = 11.69

P = 0.0000 DF = 171Both use Pooled StDev = 2.95

1. What assumptions must be met for the P-value to be accurate? And, are the assumptions met?

Two sample T for height

gender N Mean StDev SE MeanM 84 70.05 3.03 0.33F 89 64.80 2.88 0.30

95% CI for mu (M) - mu (F): ( 4.36, 6.14)T-Test mu (M) = mu (F) (vs >): T = 11.69

P = 0.0000 DF = 171Both use Pooled StDev = 2.95

2. What conclusion can we make about the average heights of male and female students?

Two sample T for height

gender N Mean StDev SE MeanM 84 70.05 3.03 0.33F 89 64.80 2.88 0.30

95% CI for mu (M) - mu (F): ( 4.36, 6.14)T-Test mu (M) = mu (F) (vs >): T = 11.69

P = 0.0000 DF = 171Both use Pooled StDev = 2.95

3. What type of error might we have made?

Two sample T for age

gender N Mean StDev SE MeanM 84 21.05 3.15 0.34F 89 20.79 2.74 0.29

95% CI for mu (M) - mu (F): ( -0.62, 1.15)T-Test mu (M) = mu (F) (vs not =): T = 0.58

P = 0.56 DF = 171Both use Pooled StDev = 2.95

4. True or false? We can conclude that the average age of males and females in the population are the same.

Two sample T for age

gender N Mean StDev SE MeanM 84 21.05 3.15 0.34F 89 20.79 2.74 0.29

95% CI for mu (M) - mu (F): ( -0.62, 1.15)T-Test mu (M) = mu (F) (vs not =): T = 0.58

P = 0.56 DF = 171Both use Pooled StDev = 2.95

5. At which of the following significance levels do we conclude that the average age differs for males and females -- 0.01, 0.05, or 0.10?

Two sample T for age

gender N Mean StDev SE MeanM 84 21.05 3.15 0.34F 89 20.79 2.74 0.29

95% CI for mu (M) - mu (F): ( -0.62, 1.15)T-Test mu (M) = mu (F) (vs not =): T = 0.58

P = 0.56 DF = 171Both use Pooled StDev = 2.95

6. What type of error might we have made?

Two sample T for age

gender N Mean StDev SE MeanM 84 21.05 3.15 0.34F 89 20.79 2.74 0.29

95% CI for mu (M) - mu (F): ( -0.62, 1.15)T-Test mu (M) = mu (F) (vs not =): T = 0.58

P = 0.56 DF = 171Both use Pooled StDev = 2.95

7. True or false? The p-value, 0.56, is the probability that the average ages are the same.

8. Which confidence interval will be longer, A or B? (Assume everything else is the same.)

A: a 99% confidence interval

B: a 90% confidence interval

9. Which confidence interval will be longer, A or B? (Assume everything else is the same.)

A: based on a standard deviation of 10

B: based on a standard deviation of 12

10. A random sample of 64 students have an average IQ of 100 with a standard deviation of 16. What is the upper limit of a 95% confidence interval for the average IQ of all students? (Use Z = 2.)

11. Observational study or experiment?

A study compared the current health status of soldiers in the Persian Gulf War to soldiers who were not in the Gulf War.

12. Why should you, whenever possible, do an experiment over an observational study?

Test of p = 0.1 vs p not = 0.1

Success = Yes

Variable X N Sample p 95.0 % CIhispanic 6 175 0.034286 (0.007326, 0.061245)

Z-Value P-Value-2.90 0.004

13. What assumption must be met for the P-value to be accurate? And, is the assumption met?

Test of p = 0.1 vs p not = 0.1

Success = Yes

Variable X N Sample p 95.0 % CIhispanic 6 175 0.034286 (0.007326, 0.061245)

Z-Value P-Value-2.90 0.004

14. True or false? A reasonable guess at the percentage of Hispanics in the student population is 10%.

15. How would you analyze the data to answer the question: Do seniors earn higher semester grade point averages than freshmen?

16. The average cholesterol level of healthy American adults is 200 with a standard deviation of 10. If random samples of 100 people were repeatedly taken, what would the “sampling distribution” of the mean look like? (Specify the shape of the distribution, the mean, and the standard deviation.)

17. How would you analyze the data to answer the following question: Do a higher percentage of Alaskans commit suicide than non-Alaskans?

18. How would you analyze the data to answer the following question: Do PSU students drink, on average, more than 1 cup of coffee per day during finals week? (During finals week, a sample of students will record how many cups of coffee they drink each day.)

19. Is the average number of credits taken by students more than 16? The average number of credits taken by a random sample of 64 students is 18 with a standard deviation of 4. Describe the p-value in English.

20. Is the average number of credits taken by students more than 16? The average number of credits taken by a random sample of 64 students is 18 with a standard deviation of 4. What is the value of the Z test statistic (that is obtained when calculating the p-value)?

21. What is the median maximal oxygen uptake?

Stem-and-leaf of Uptake N = 9Leaf Unit = 1.0

1 3 1 1 3 1 3 2 3 7 4 3 89 (2) 4 11 3 4 3 4 5 2 4 7 1 4 8

22. What is the median blood hemoglobin level?

Stem-and-leaf of Hemo N = 10Leaf Unit = 0.10

1 0 5 4 1 024 (3) 1 557 3 2 04 1 2 1 3 1 3 6

30 40 50

Uptake

23. True or false? Maximal oxygen uptake is normally distributed.

24. It is known that cholesterol level of American people is normally distributed with mean 200 and standard deviation 20. An individual has a cholesterol level of 280. Is this an unusual value? Justify your answer.

25. A certain drug treatment cures 90% of the cased of hookworm in children. Suppose that 20 children suffering from hookworm are to be treated, and that the children can be regarded as a random sample from the population. Set up how you’d calculate the probability that all 20 will be cured.

26. Same problem. A certain drug treatment cures 90% of the cased of hookworm in children. Suppose that 20 children suffering from hookworm are to be treated, and that the children can be regarded as a random sample from the population. Set up how you’d calculate the probability that more than 17 will be cured.

27. A survey shows that 40% of all convenience-store shoppers buy milk, 30% buy bread, and 25% buy both milk and bread. What percentage of shoppers buy either milk or bread?

28. Same problem. A survey shows that 40% of all convenience-store shoppers buy milk, 30% buy bread, and 25% buy both milk and bread. If a randomly selected person buys bread, what is the probability that the person will also buy milk?

Rows: Gender Columns: ETLife No Yes All M 7.32 92.68 100.00 18.75 57.58 50.00 3.66 46.34 50.00 F 31.71 68.29 100.00 81.25 42.42 50.00 15.85 34.15 50.00 All 19.51 80.49 100.00 100.00 100.00 100.00 19.51 80.49 100.00 Cell Contents -- % of Row % of Col % of Tbl

29. What percentage of males believe in extra-terrestrial life?

Rows: Gender Columns: ETLife No Yes All M 7.32 92.68 100.00 18.75 57.58 50.00 3.66 46.34 50.00 F 31.71 68.29 100.00 81.25 42.42 50.00 15.85 34.15 50.00 All 19.51 80.49 100.00 100.00 100.00 100.00 19.51 80.49 100.00 Cell Contents -- % of Row % of Col % of Tbl

30. What percentage of students are male and believe in extra-terrestrial life?

Rows: Gender Columns: ETLife No Yes All M 7.32 92.68 100.00 18.75 57.58 50.00 3.66 46.34 50.00 F 31.71 68.29 100.00 81.25 42.42 50.00 15.85 34.15 50.00 All 19.51 80.49 100.00 100.00 100.00 100.00 19.51 80.49 100.00 Cell Contents -- % of Row % of Col % of Tbl

31. What percentage of students who believe in extra-terrestrial life are female?

Rows: Gender Columns: ETLife No Yes All M 7.32 92.68 100.00 18.75 57.58 50.00 3.66 46.34 50.00 F 31.71 68.29 100.00 81.25 42.42 50.00 15.85 34.15 50.00 All 19.51 80.49 100.00 100.00 100.00 100.00 19.51 80.49 100.00 Cell Contents -- % of Row % of Col % of Tbl

32. What percentage of students are either male or believe in extra-terrestrial life?

33. 10% of alcoholics develop cirrhosis of the liver, while 1% of non-alcoholics do. How many times more likely are alcoholics than non-alcoholics to develop cirrhosis of the liver? That is, what is the relative risk?

34. Same problem. 10% of alcoholics develop cirrhosis of the liver, while 1% of non-alcoholics do. What is the increased risk?

35. Same problem. 10% of alcoholics develop cirrhosis of the liver, while 1% of non-alcoholics do. If an alcoholic, what are the odds of developing cirrhosis of the liver?