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Module 6 Review
AP Statistics
#1. Compute a 95% confidence interval for a population mean given a sample mean of 37. Assume that the population
standard deviation is known to be 10 and the sample size is 50.
#2. How does changing the sample size affect the margin of error?
#3. Studies have shown that 30% of adults aged 55-70 know who Miley Cyrus is. You think that in a large hip town like
Orlando, this percentage is higher. What hypotheses would you test if you wish to perform a statistical significance test?
#4. When performing a test of significance, what provides strong evidence against the null hypothesis?
#5. A significance test gives a P-value of 0.04. From this we can
(a) Reject H0 at the 1% significance level
(b) Reject H0 at the 5% significance level
(c) Say that the probability that H0 is false is 0.04
(d) Say that the probability that H0 is true is 0.04
#6. An agricultural researcher plants 25 plots with a new variety of corn. The average yield for these plots is 150 bushels
per acre. Assume that the yield per acre for the new variety of corn follows a normal distribution with unknown mean 
and standard deviation  = 10 bushels per acre. Find a 90% confidence interval for , the mean yield of bushels per acre.
#7. If we find our results to be statistically significant, does this also mean that they are practically significant? Explain.
#8. Describe the following:
-
The Placebo Effect
-
The Hawthorne Effect
#9. It is believed that the average amount of money spent per U.S. household per week on food is about $98, with
standard deviation $10. A random sample of 100 households in a certain affluent community yields a mean weekly
food budget of $100. We want to test the hypothesis that the mean weekly food budget for all households in this
community is higher than the national average.
(a) Perform a significance test at the   0.05 significance level. Follow all steps.
(b) Describe a Type I error in the context of this problem. What is the probability of making a Type I error?
(c) Describe a Type II error in the context of this problem.
#10. It is believed that the average number of hours per day high school students watch tv is 2. A significance test was
performed to test the null hypothesis H0: µ = 2 versus the alternative Ha: µ  2. The test statistic is z = 1.40. Find
the p-value and interpret this p-value in the context of the problem.
#11. You have measured the systolic blood pressure of a random sample of 25 employees of a company located near
you. A 95% confidence interval for the mean systolic blood pressure for the employees of this company is (122, 138).
Which of the following statements gives a valid interpretation of this interval?
(a) 95% of the sample of employees has a systolic blood pressure between 122 and 138.
(b) 95% of the population of employees has a systolic blood pressure between 122 and 138.
(c) If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the
population mean systolic blood pressure.
(d) The probability that the population mean blood pressure is between 122 and 138 is .95.
(e) If the procedure were repeated many times, 95% of the sample means would be between 122 and 138.
#12. You want to estimate the mean SAT score for a population of students with a 90% confidence interval. Assume
that the population standard deviation is  = 100. If you want the margin of error to be approximately 10, what size
sample will you need?
#13. You ask 15 households in your neighborhood how many pieces of mail they receive each day. You find that the
average is 4. Suppose the standard deviation for the population is 1.2. You want to find the mean number of pieces of
mail for all households in your neighborhood.
a) What is the upper critical value for a 96% confidence interval?
b) What is the confidence level?
c) Calculate the 96% confidence interval.
#14. There are many ways to measure the reading ability of children. Research designed to improve reading
performance is dependent on good measures of the outcome. One frequently used test is the DRP or Degree of
Reading Power. A researcher suspects that the mean score µ of all third graders in Henrico County Schools is
different from the national mean, which is 32. To test her suspicion, she administers the DRP to an SRS of 44
Henrico County third-grade students. Their scores were:
40
47
52
47
26
19
25
35
39
26
35
48
14
35
35
22
42
34
33
33
18
15
29
41
25
44
34
51
43
40
41
27
46
38
49
14
27
31
28
54
19
46
52
45
She then asked Minitab to calculate some descriptive statistics from this data set:
MTB > Describe 'DRPscore'.
DRPscore
N MEAN MEDIAN TRMEAN STDEV SEMEAN
44 35.09 35.00
35.25
11.19 1.69
DRPscore
MIN MAX
Q1
Q3
14.00 54.00 26.25 44.75
You may assume that DRP scores are approximately normal, and that the standard deviation of scores in Henrico County
Schools is known to be  = 11.
(a) Construct a 95% confidence interval for the mean DRP score in Henrico County Schools. Follow all steps.
(b) Use the confidence interval you constructed in (a) to test the researcher’s claim. Be sure to state your
hypotheses and your significance level.