1. AP Stats Review

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

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

4. It is known that, for a particular school, math scores are normally distributed. A random sample of the scores of 10 students of each gender yielded the values shown below. Do these data indicate a difference in the mean performance of all the boys and girls in this school at the 5% level of significance? Give the formula for this test Give the assumptions for this test Hypothesis
Girls 90 80 70 75 87 92 86 61 94
100
Boys 96 85 72 63 95 68 98

5. 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

6. What’s the difference between blocking & stratifying?

7. Find & interpret the correlation coefficient.
Predictor Coef SE Coef T P
Constant
height
S = R-Sq = 80.1% R-Sq(adj) = 76.8%
Find & interpret the correlation coefficient.

8. A pharmaceutical company claims that 50% of adult males living in a city in the Midwest get at least two colds per year. A random sample of 100 adult males living the city of interest reported that only 42% of them experience two or more colds. Do these data indicate (at the 5% sig. level) that the true proportion of people who get more than 2 colds per year is less than 50%? Give the formula Give the assumptions Give the hypothesis

9. Name each type of sampling method: A
Name each type of sampling method: A. Code every member of a population and select 100 randomly chosen members. B. Divide a population by gender and select 50 individuals randomly from each group. C. Select five homerooms at random from all of the homerooms in a large high school. D. Choose every 10th person who enters the school. E. Choose the first 100 people who enters the school.

10. Find an estimate of the population slope. (Use 95%)
Predictor Coef SE Coef T P
Constant
height
S = R-Sq = 80.1% R-Sq(adj) = 76.8%
Find an estimate of the population slope. (Use 95%)

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

12. The specifications fro the length of a part in a manufacturing process call for a mean of cm. A simple random sample of 50 parts indicates a mean of cm with a standard deviation of 0.54 cm. Find the probability that a random sample of 50 of the parts will have a mean of cm or more.

13. Find & interpret the coefficient of determination.
Predictor Coef SE Coef T P
Constant
height
S = R-Sq = 80.1% R-Sq(adj) = 76.8%
Find & interpret the coefficient of determination.

14. Students were give a pretest at the beginning of the unit on linear equations and the same exam as a post-test at the end of the unit. Do these data indicate at the 5 % level, that there was an improvement in the scores once the instruction on the unit was completed? Give the formula Give the assumptions Give the hypothesis
Pre 75 82 45 91 65 85 78 64
Post 81 55 93 86 66

15. 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.

16. Find & interpret the slope
Predictor Coef SE Coef T P
Constant
height
S = R-Sq = 80.1% R-Sq(adj) = 76.8%
Find & interpret the slope

17. What is the p-value?

18. Explain the power of a test.

19. 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%

20. Find the residual amount if the observed value was (68,37).
Predictor Coef SE Coef T P
Constant
height
S = R-Sq = 80.1% R-Sq(adj) = 76.8%
Find the residual amount if the observed value was (68,37).

21. 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%

22. Predictor Coef StDev T P Constant 12.96 6.228 2.08 0.045 ProbSolv
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%

23. 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%

24. Predictor Coef StDev T P Constant 12.96 6.228 2.08 0.045 ProbSolv
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%

25. What kind of test is this?
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
What kind of test is this?
What is the expected number of males who prefer chocolate?
What is the degrees of freedom?
What assumptions must be made?

26. 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.

27. Can you prove that a linear relationship exists? Show it!
Predictor Coef SE Coef T P
Constant
height
S = R-Sq = 80.1% R-Sq(adj) = 76.8%
Can you prove that a linear relationship exists? Show it!

28. 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.

29. 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?

30. 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.

31. 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?

32. 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.

33. 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) = Find the probability that the entire system works properly.

34. 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) = What is the probability that at least one of the four components will work properly?