AP STATISTICS
Unit VI Review
Using the t-tables, software, or a calculator, estimate the critical value of t for the given confidence interval
and degrees of freedom.
1. 90% confidence interval with df = 4.
Use the t-tables, software, or a calculator to estimate the indicated P-value.
2. P-value for t ≤ 1.76 with 24 degrees of freedom
Interpret the confidence interval.
3. A random sample of clients at a weight loss center were given a dietary supplement to see if it would promote
weight loss. The center reported that the 100 clients lost an average of 44 pounds, and that a 95% confidence
interval for the mean weight loss this supplement produced has a margin of error of ±7 pounds.
Use the given sample data to construct the indicated confidence interval for the population mean.
4. Thirty randomly selected students took the calculus final. If the sample mean was 82 and the standard deviation
was 6.0, construct a 99% confidence interval for the mean score of all students.
5. A random sample of 30 long distance runners aged 20-25 was selected from a running club. The resting heart
rates (in beats per minute) of the runners are shown below. Estimate the mean resting heart rate for the
population of long distance runners aged 20-25. Give the 95% confidence interval.
62 70 61 64 75 54 72 68 74 54
75 70 62 66 79 73 81 60 66 76
67 62 66 69 70 86 76 60 53 71
Determine the margin of error in estimating the population parameter.
6. Based on a sample of size 48, a 95% confidence interval for the mean score of all students on an aptitude test is
from 65.3 to 72.7.
Classify the hypothesis test as lower-tailed, upper-tailed, or two-sided.
7. A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer
advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than
this.
For the given hypothesis test, explain the meaning of a Type I error or a Type II error, as specified.
8. In the past, the mean running time for a certain type of flashlight battery has been 8.0 hours. The manufacturer
has introduced a change in the production method and wants to perform a hypothesis test to determine whether
the mean running time has increased as a result. The hypotheses are:
H0 : μ = 8.0 hours
HA : μ > 8.0 hours
Explain the result of a Type II error.
Use a hypothesis test to test the given claim.
9. Is the mean weight of female college students still 132 pounds? To test this, you take a random sample of 20
students, finding a mean of 137 pounds with a standard deviation of 14.2 pounds. Use a significance level of 0.1.
Provide an appropriate response.
10. You want to determine if the average gas price in your city has exceeded $2.15 per gallon for regular gas. You
take a random sample of prices from 8 gas stations, recording the following prices:
$2.13, $2.10, $1.80, $2.09, $2.17, $2.12, $2.10, $2.11. Have the conditions and assumptions for inference
been
met?
11. Suppose you have obtained a confidence interval for μ, but wish to obtain a greater degree of precision. Which
of the following would result in a narrower confidence interval?
A. Increasing the sample size while keeping the confidence level fixed
B. Decreasing the sample size while keeping the confidence level fixed
C. Increasing the confidence level while keeping the sample size fixed
D. Decreasing the confidence level while keeping the sample size fixed
Construct the indicated confidence interval for the difference between the two population means. Assume that the
assumptions and conditions for inference have been met.
12. A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by
following a particular diet. Use the sample data below to construct a 99% confidence interval for μ1 - μ 2 where
μ1 and μ2 represent the mean for the treatment group and the control group respectively.
Treatment Group
n1 = 85
x1 = 189.1
s1 = 38.7
Control Group
n2 = 75
x2 = 203.7
s2 = 39.2
Interpret the given confidence interval.
13. A survey was conducted to determine the difference in gasoline mileage for two types of trucks. A random
sample was taken for each model of truck, and the mean gasoline mileage, in miles per gallon, was calculated. A
98% confidence interval for the difference in the mean mileage for model A trucks and the mean mileage for
model B trucks,
μA - μB, was determined to be (2.6, 4.5).
Provide an appropriate response.
14. A researcher is interested in the academic performance differences between individuals using an optimistic
versus a pessimistic approach to their studies. If the researcher fails to find a significant difference, when in fact
one exists in the population, what has happened?
15. A philosophy professor wants to find out whether the mean age of the men in his large lecture class is equal to
the mean age of the women in his classes. After collecting data from a random sample of his students, the
professor tested the hypothesis
H0: μm - μw = 0 against the alternative HA: μm - μw ≠ 0.
The P-value for the test was 0.003. What does this result mean?
Construct the indicated confidence interval for the difference between the two population means. Assume that the
assumptions and conditions for inference have been met.
16. 120 Brand X oil filters and 90 Brand Y oil filters were tested for milligrams of residue, with the following
results. Find a 95% confidence interval for μY - μX.
Sample
Mean
Brand X
Brand Y
A
C
Sample
Standard
Deviation
B
D
A = 5.9 B = 0.87
C = 4.7 D = 0.86
Indicate the correct test procedure and reasoning.
17. A researcher is interested in investigating whether people perform better at dexterity tests while listening to
classical music or to no music. She designs a dexterity test, and first gives it to her participants while classical
music is playing, and then while no music is playing.
Use the paired t-interval procedure to obtain the required confidence interval for the mean difference. Assume that
the conditions and assumptions for inference are satisfied.
18. An agricultural company wanted to know if a new insecticide would increase corn yields. Eight test plots
showed an average increase of 3.125 bushels per acre. The standard deviation of the increases was 2.911 bushels
per acre. Determine a 99% confidence interval for the mean increase in yield.
19. A test of writing ability is given to a random sample of students before and after they completed a formal
writing course. The results are given below. Construct a 99% confidence interval for the mean difference
between the before and after scores.
Before 70 80 92 99 93 97 76 63 68 71 74
After 69 79 90 96 91 95 75 64 62 64 76
Interpret the given confidence interval.
20. Ten different families were tested for the average number of gallons of water they used per day before and after
viewing a conservation video. A 90% confidence interval for the difference of the means after and before the
training, μA - μB, was determined to be (-10.3, -4.1).
21. A study was conducted to determine if people consume more calories when they eat dinner while watching
television. A random sample of ten people was selected to eat dinner one night in the dining room and the next
night while watching television in the family room. The caloric content of their dinners was measured, and a
95% confidence interval for the difference in the means with and without the television, μTV - μ, was determined
to be (-30, 210).
22. At one SAT test site students taking the test for a second time volunteered to inhale supplemental oxygen for
10 minutes before the test. In fact, some received oxygen, but others (randomly assigned) were given just
normal air. Test results showed that 42 of 66 students who breathed oxygen improved their SAT scores,
compared to only 35 of 63 students who did not get the oxygen. Which procedure should we use to see if there
is evidence that breathing extra oxygen can help test-takers think more clearly?
23. A credit union took a random sample of 40 accounts and obtained the following 90% confidence interval for
the mean checking account balance at the institution:
$2199 < μ(balance) < $3820.
(A) About 9 out of 10 people have a checking account balance between $2199 and $3820.
(B) If we took random samples of checking accounts at this credit union, about nine out of ten
of them would produce this confidence interval.
(C) We are 90% sure that the mean balance for checking accounts in the sample was between
$2199 and $3820.
(D) We are 90% confident that the mean checking account balance in the U.S. is between $2199
and $3820.
(E) We are 90% confident that the mean checking account balance at this credit union is
between $2199 and $3820, based on this sample.
Use the given sample data to construct the indicated confidence interval for the population mean.
24.
n = 12, x = 23.8, s = 5.6
Find a 99% confidence interval for the mean.
25.
A sample of 64 statistics students at a small college had a mean mathematics ACT score of 27 with a standard
deviation of 6. Find a 95% confidence interval for the mean mathematics ACT score for all statistics students
at this college.
Do you know when to use a paired t-test as opposed to a 2-sample t-test?
Can you perform both of these tests completey?
Did you review the problems on the quiz ABC questions that we have done in class for each chapter?
Did you pay attention to the free response and investigative task question explanations given to you after
the mock AP exam on Saturday?
Multiple Choice
1. 2.132
2. 0.9544
3. We are 95% confident that the mean weight loss produced by the supplement in weight loss center
clients is between 37 and 51 pounds.
4. (78.98, 85.02)
5. (65.0, 71.1)
6. 3.7
7. Lower-tailed
8. The manufacturer will decide the mean battery life is 8.0 hours when in fact it is greater than 8.0 hours.
9. Fail to reject the null hypothesis of μ=132 with a P-value of 0.1318. There is not sufficient evidence that
the weight of female students has changed.
10. No, the nearly normal condition is not met.
11. A and D
12. (-30.7, 1.5)
13. Based on this sample, we are 98% confident that the average mileage for model A trucks is between 2.6
and 4.5 miles per gallon higher than the average mileage for model B trucks.
14. a Type 2 error has been made.
15. It is very unlikely that the professor would see results like these if the mean age of men was equal to the
mean age of women.
16. (-1.44, -0.96)
17. Paired t-test, since there are two sets of measurements on the same subjects, providing a natural linking.
18. (-0.476, 6.726)
19. (-0.5,4.5)
20. Based on this sample, we are 90% confident that the average decrease in daily water consumption after
viewing the conservation video is between 4.1 and 10.3 gallons.
21. Based on this sample, we are 95% confident that the average caloric content is between 30 fewer and
210 more calories when people eat dinner in front of the television compared to dinner in the dining
room.
22. 2-proportion z-test
23. E
24. (18.78, 28.82)
25. (25.5, 28.5)