ap stats review. assume that the probability that a baseball player will get a hit in any one at-bat...

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Assume that the probability that a baseball player will get a hit in any one at-bat is 0.250. Give an expression for the probability that his first hit will next occur on his 5th at bat? What kind of distribution is this?

A symmetric, mound-shaped distribution has a mean of 70 and a standard deviation of 10, find the 16th percentile score.

Girls 90 80 70 75 87 92 86 61 94 100

Boys 70 75 96 92 85 72 63 95 68 98

The table below give the estimated marginal cost for a piece of furniture. Find the residual amount for 400 units.

Units 100 200 300 400 500 600

Marginal Cost $300 $250 $220 $200 $180 $175

What’s the difference between blocking & stratifying?

Blocking is used in experiments while stratifying is used in surveys.

Find & interpret the correlation coefficient.

Predictor Coef SE Coef T PConstant -4.792 8.521 -0.56 0.594height 0.6077 0.1236 4.92 0.003

S = 0.932325 R-Sq = 80.1% R-Sq(adj) = 76.8%

Name each type of sampling method:A. Code every member of a population and select 100 randomly chosen members.

Simple Random Sample (SRS)

B. Divide a population by gender and select 50 individuals randomly from each group.

Stratified

C. Select five homerooms at random from all of the homerooms in a large high school.

Cluster

D. Choose every 10th person who enters the school.Systematic

E. Choose the first 100 people who enters the school.Convenience

Find an estimate of the population slope if sample is

size 10. (Use 95%)

Predictor Coef SE Coef T PConstant -4.792 8.521 -0.56 0.594height 0.6077 0.1236 4.92 0.003

S = 0.932325 R-Sq = 80.1% R-Sq(adj) = 76.8%

If I increase the significance level, what happens to the power of the test? Explain.

If I increase alpha, then Beta decreases. Thus the power of the test (1-Beta) will Increase.

The specifications fro the length of a part in a manufacturing process call for a mean of 11.25 cm. Find the probability that a random sample of 50 of the parts will have a mean of 11.56 cm or more if the standard deviation is 0.54.

Find & interpret the coefficient of determination.

Predictor Coef SE Coef T PConstant -4.792 8.521 -0.56 0.594height 0.6077 0.1236 4.92 0.003

S = 0.932325 R-Sq = 80.1% R-Sq(adj) = 76.8%

Pre 75 82 45 91 65 75 85 82 78 64

Post 78 81 55 93 65 78 81 86 82 66

A preliminary study has indicated that the standard deviation of a population is approximately 7.85 hours. Determine the smallest sample size needed to be within 2 hours of the population mean with 95% confidence.

Find & interpret the slope

Predictor Coef SE Coef T PConstant -4.792 8.521 -0.56 0.594height 0.6077 0.1236 4.92 0.003

S = 0.932325 R-Sq = 80.1% R-Sq(adj) = 76.8%

Slope = 0.6077

For every addition inch in height, the (y-variable) increases 0.6077 units.

What is the p-value?

It is the probability that I got this sample, as extreme as it may be, if the Ho was really true.

Explain the power of a test.

It is the probability that rejecting the Ho is the correct decision. It is found by calculating 1 – Beta.

A midterm exam in Applied Mathematics consist of problems in 8 topical area. One of the teachers believe that the most important of these, and the best indicator of overall performance, is the section on problem solving. She analyzes the scores of 36 randomly chosen students using MINITAB, comparing the total score to the problem-solving subscore.

Give the equation for the least squares regression line.

Predictor Coef StDev T P

Constant 12.96 6.228 2.08 0.045

ProbSolv 4.0162 0.5393 7.45 0.000

s = 11.09 R-Sq = 62.0% R-Sq (adj)= 60.9%

Find the residual amount if the observed value was

(68,37).

Predictor Coef SE Coef T PConstant -4.792 8.521 -0.56 0.594height 0.6077 0.1236 4.92 0.003

S = 0.932325 R-Sq = 80.1% R-Sq(adj) = 76.8%

She analyzes the scores of 36 randomly chosen students using MINITAB, comparing the total score to the problem-solving subscore.

Find and interpret the coefficient of determination.

Predictor Coef StDev T P

Constant 12.96 6.228 2.08 0.045

ProbSolv 4.0162 0.5393 7.45 0.000

s = 11.09 R-Sq = 62.0% R-Sq (adj)= 60.9%

She analyzes the scores of 36 randomly chosen students using MINITAB, comparing the total score to the problem-solving subscore.

Find and interpret the slope.

Predictor Coef StDev T P

Constant 12.96 6.228 2.08 0.045

ProbSolv 4.0162 0.5393 7.45 0.000

s = 11.09 R-Sq = 62.0% R-Sq (adj)= 60.9%

She analyzes the scores of 36 randomly chosen students using MINITAB, comparing the total score to the problem-solving subscore.

Find an estimate for the slope. Justify your answer.

Predictor Coef StDev T P

Constant 12.96 6.228 2.08 0.045

ProbSolv 4.0162 0.5393 7.45 0.000

s = 11.09 R-Sq = 62.0% R-Sq (adj)= 60.9%

She analyzes the scores of 36 randomly chosen students using MINITAB, comparing the total score to the problem-solving subscore.

Can you justify that there is a linear relationship – using statistical justification? Show it!

Predictor Coef StDev T P

Constant 12.96 6.228 2.08 0.045

ProbSolv 4.0162 0.5393 7.45 0.000

s = 11.09 R-Sq = 62.0% R-Sq (adj)= 60.9%

Reject Ho since pval < alpha (0.05). There is a linear relationship between Problem Solving subscore and test score.

The table below specifies favorite ice cream flavors by gender. Is there a relationship between favorite flavor and gender?

  Male Female

Chocolate 32 16

Vanilla 14 4

Strawberry 3 10

A study of 20 teachers in a school district indicated that the 95% confidence interval for the mean salary of all teachers in that school district is ($38,945, $41, 245).

What assumptions must be true for this confidence interval to be valid?

A. No assumptions are necessary. The Central Limit Theorem applies.B. The sample is randomly selected from a population of

salaries that is a t-distribution.C. The distribution of the sample means is approximately

normal.D. The distribution of teachers’ salaries in the school district is approximately normal. E. The standard deviation of the distribution of teachers’

salaries in the school district is known.

Can you prove that a linear relationship exists? Show

it!

Predictor Coef SE Coef T PConstant -4.792 8.521 -0.56 0.594height 0.6077 0.1236 4.92 0.003

S = 0.932325 R-Sq = 80.1% R-Sq(adj) = 76.8%

Reject Ho since pval < alpha (0.05). There is a linear relationship between height and (y variable).

A study of 20 teachers in a school district indicated that the 95% confidence interval for the mean salary of all teachers in that school district is ($38,945, $41, 245).

Explain what is meant by the 95% confidence interval.

Explain what is meant by the 95% confidence level.

We are 95% confident that the mean salary of all teachers in the school district is between $38,945 and $41,245.

If we repeat this process over and over, 95% of the intervals formed will contain the true population mean.

If an NFL quarterback’s pass completion percent is 79%, what is the probability that he will only complete 15 of 30 passes in his next game?

If an NFL quarterback’s pass completion percent is 79%, what is the probability that he will only complete 15 of 30 passes in his next game?

Give me two other ways of stating the formula for the previous problem.

If an NFL quarterback’s pass completion percent is 79%, what is the probability that he will only complete 15 of 30 passes in his next game?

Does this problem really meet the criteria for a binomial variable?

Yes – It is binomial – 2 possibilities (complete or don’t complete)

Independent n is fixed success probability does not change

A candy make coats her candy with one of three colors: red, yellow, or blue, in published proportions of 0.3, 0.3, and 0.4 respectively. A simple random sample of 50 pieces of candy contained 8 red, 20 yellow, and 22 blue pieces. Is the distribution of colors consistent with the published proportions. Give appropriate statistical evidence to justify your answer.

Obs Exp X^28 15 3.2667

20 15 1.666722 20 0.2

5.13

P1=prop redP2=prop yellowP3=prop blue

All cells >5Chi Sq Goodness of Fit

The primary air exchange system on a proposed spacecraft has four separate components (A, B, C, D) that all must work properly for the system to operate well. Assume that the probability of any one component working is independent of the other components. It has been shown that the probabilities of each component working are P(A) = 0.95, P(B) = 0.90, P(C )= 0.99, and P(D) = 0.90.

Find the probability that the entire system works properly.

The primary air exchange system on a proposed spacecraft has four separate components (A, B, C, D) that all must work properly for the system to operate well. Assume that the probability of any one component working is independent of the other components. It has been shown that the probabilities of each component working are P(A) = 0.95, P(B) = 0.90, P(C )= 0.99, and P(D) = 0.90.

What is the probability that at least one of the four components will work properly?

The only time you don’t have at least one is when you have none.

P(at least 1) = 1 – P(none) = 1 – [0.05 * 0.1 * 0.01 * 0.1]

= 1 – 0.00005 = 0.999995