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FINAL REVIEW
1. In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery.
The standard error of the sample proportion is approximately
A. 0.0094
B. 0.0306
C. 0.0353
D. 0.2500
E. 6.1237
2. To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed a total
of n times and the mean of the weighings is computed. Suppose the scale readings are Normally distributed with unknown
mean and standard deviation
= 0.01 g. How large should n be so that a 95% confidence interval for
has a margin of
error of ± 0.0001?
A. 100
B. 196
C. 27,061
D. 10,000
E. 38,416
3. The weights of 9 men have mean
= 175 pounds and standard deviation s = 15 pounds. What is the standard error of the
mean?
A. 58.3
B. 15
C. 5
D. 1.67
E. 1.29
4. The college newspaper of a large Midwestern university periodically conducts a survey of students on campus to
determine the attitude on campus concerning issues of interest. Pictures of the students interviewed along with quotes of
their responses are printed in the paper. Students are interviewed by a reporter “roaming” the campus selecting students to
interview “haphazardly.” On a particular day the reporter interviews five students and asks them if they feel there is adequate
student parking on campus. Four of the students say, “no.” Which of the following conditions for inference about a
proportion using a confidence interval are violated in this example?
I. The data are an SRS from the population of interest.
II. The population is at least ten times as large as the sample.
III.
A. I only
10 and
B. II only
.
C. III only
D. I and III
E. All three conditions are violated
5. In a test of H0: p = 0.7 against Ha: p
0.7, a sample of size 80 produces z = 0.8 for the value of the test statistic. Which of
the following is closest to the P-value of the test?
A. 0.2090
B. 0.2119
C. 0.4238
D. 0.4681
E. 0.7881
6. An opinion poll asks a simple random sample of 100 college seniors how they view their job prospects. In all, 53 say
“good.” Does the poll give convincing evidence to conclude that more than half of all seniors think their job prospects are
good? If p = the proportion of all college seniors who say their job prospects are good, what are the hypotheses for a test to
answer this question?
A. H0: p = 0.5, Ha: p > 0.5.
B. H0: p > 0.5, Ha: p = 0.5.
C. H0: p = 0.5, Ha: p
0.5.
D. H0: p = 0.5, Ha: p < 0.5.
E. H0: p 0.5, Ha: p > 0.5.
7. In a test of H0: µ = 100 against Ha: µ
100, a sample of size 10 produces a sample mean of 103 and a P-value of 0.08.
Which of the following is true at the 0.05 level of significance?
A. There is sufficient evidence to conclude that µ 100.
B. There is sufficient evidence to conclude that µ = 100.
C. There is insufficient evidence to conclude that µ = 100.
D. There is insufficient evidence to conclude that µ 100.
E. There is sufficient evidence to conclude that µ > 103.
8. An appropriate 95% confidence interval for µ has been calculated as ( 0.73, 1.92 ) based on n = 15 observations from a
population with a Normal distribution. If we wish to use this confidence interval to test the hypothesis H0: µ = 0 against Ha: µ
0, which of the following is a legitimate conclusion?
A. Reject H0 at the
= 0.05 level of significance.
B. Fail to reject H0 at the
= 0.05 level of significance.
C. Reject H0 at the
= 0.10 level of significance.
D. Fail to reject H0 at the
= 0.10 level of significance.
E. We cannot perform the required test since we do not know the value of the test statistic.
9. Which of the following increases the power of a significance test?
A. Using a two-tailed test instead of a one-tailed test.
B. Decreasing the size of your sample.
C. Finding a way to increase the population standard deviation .
D. Increasing the significance level .
E. Perform the test many times using the same data.
10. Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually vary slightly from
bag to bag and are Normally distributed with mean . A representative of a consumer advocacy group wishes to see if there
is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses
A Type I error in this situation would mean
A. concluding that the bags are being underfilled when they actually aren’t.
B. concluding that the bags are being underfilled when they actually are.
C. concluding that the bags are not being underfilled when they actually are.
D. concluding that the bags are not being underfilled when they actually aren’t.
E. none of these
11. A significance test was performed to test the null hypothesis
: p = 0.5 versus the alternative
Ha: p > 0.5. The test statistic is z = 1.40. Which of the following is closest to the P-value for this test?
A. 0.0808
B. 0.1492
C. 0.1616
D. 0.2984
E. 0.9192
12. The mean time it takes for a person to experience pain relief from aspirin is 25 minutes. A new ingredient is added to help
speed up relief. Let µ denote the mean time to obtain pain relief with the new product. An experiment is conducted to verify
if the new product works more quickly. What are the null and alternative hypotheses for the appropriate test of significance?
A. H0 : µ = 25 vs. Ha : µ 25
B. H0 : µ = 25 vs. Ha : µ < 25
C. H0 : µ < 25 vs. Ha : µ = 25
D. H0 : µ < 25 vs. Ha : µ > 25
E. H0 : µ = 25 vs. Ha : µ > 25
13. A test of
produces a sample mean of
level, which of the following is an appropriate conclusion?
A. There is sufficient evidence to conclude that µ < 60.
B. There is sufficient evidence to conclude that µ = 60.
C. There is insufficient evidence to conclude that µ = 60.
D. There is insufficient evidence to conclude that µ 60.
E. There is sufficient evidence to conclude that µ 60.
and a P-value of 0.04. At an α = 0.05
14. A city planner is comparing traffic patterns at two different intersections. He randomly selects 12 times between 6 am
and 10 pm, and he and his assistant count the number of cars passing through each intersection during the 10-minute interval
that begins at that time. He plans to test the hypothesis that the mean difference in the number of cars passing through the
two intersections during each of those 12 times intervals is 0. Which of the following is appropriate test of the city planner’s
hypothesis?
A. Two-proportion z-test
B. Two-sample z-test
C. Matched pairs t-test
D. Two proportion t-test
E. Two-sample t-test
Scenario 11-1
A well-known chewing gum maker wants to determine if any of its four flavors of gum are more popular than the others. A
random sample of 80 people who say they chew gum regularly is asked to identify their favorite flavor of gum. Here are the
results:
Flavor
Frequency
Peppermint
25
Cinnamon
19
Wintergreen
22
Spearmint
14
15. Use Scenario 11-1. Which of the following would be an appropriate null hypothesis for the company to test?
A.
B. The observed counts are all equal to 20.
C. Flavor preferences are evenly distributed across the four flavors.
D. At least one of the four flavor preferences is different from the other three.
E. The observed counts are equal to the expected counts.
16. Use Scenario 11-1. Which of the following are conditions that must be met in order to test this hypothesis using a chisquare test?
I. If p = proportion of gum-chewers in the population, then
II. All expected cell counts are greater than 5.
III. Individual observations are independent.
A. I and II only
B. II and III only
C. I and III only
D. II only
E. I, II, and III
17. Use Scenario 11-1. Which of the following represents the component of the chi-square statistic for Wintergreen?
A. 22
B.
C.
D.
E.
18. A civil engineer is testing the reliability of traffic signal controllers produced by two different companies. He has 20 sets
of controllers from each company, and he has been given clearance to install them at 40 different intersections in the city.
He randomly assigns the controllers from company A to 20 intersections and the controllers from company B to the other
intersections. The most important reason for this random assignment is that
A. randomization is a good way to create two groups of 20 intersections that are as similar as possible, so that comparisons
can be made between the two groups.
B. randomization eliminates the impact of any confounding variables.
C. randomization makes the analysis easier since the data can be collected and entered into the computer in any order.
D. randomization ensures that the study is double-blind.
E. randomization reduces the impact of outliers.
19. A Texas school district wants to compare the effectiveness of a standard AP Statistics curriculum and a new “hands-on”
AP Statistics curriculum. Two experienced teachers, Mr. Pryor and Mr. Legacy, each teach one class with the standard
curriculum and one with the new approach. Students are assigned at random to these four classes. At the end of the year, all
students take the AP Statistics exam. The subjects in this experiment are
A. Mr. Pryor and Mr. Legacy.
B. the two AP Statistics curricula.
C. the students in the four classes.
D. all students taking AP Statistics in Texas.
E. only one: AP Statistics.
20. A friend has placed a large number of plastic disks in a hat and invited you to select one at random. He informs you that
they have numbers on them, and that one of the following is the probability model for the number on the disk you have
chosen. Which one is it?
21. If P(A). = 0.24 and P(B). = 0.52 and A and B are independent, what is P(A or B)?
A. 0.1248
B. 0.28
C. 0.6352
D. 0.76
E. not enough information
22. People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative
blood. Only 7.2% of the American population has O-negative blood. If 10 people appear at random to give blood, what is
the probability that at least 1 of them is a universal donor?
A. 0
B. 0.280
C. 0.526
D. 0.720
E. 1
23. In your top dresser drawer are 6 blue socks and 10 grey socks, unpaired and mixed up. One dark morning you pull two
socks from the drawer (without replacement, of course!). What is the probability that the two socks match?
A. 0.075
B. 0.375
C. 0.450
D. 0.500
E. 0.550
24. A business evaluates a proposed venture as follows. It stands to make a profit of $10,000 with probability 3/20, to make a
profit of $5000 with probability 9/20, to break even with probability 5/20, and to lose $5000 with probability 3/20. The
expected profit in dollars is
A. 1500.
B. 0.
C. 3000.
D. 3250.
E. –1500.
25. A set of 10 cards consists of 5 red cards and 5 black cards. The cards are shuffled thoroughly and you turn cards over,
one at a time, beginning with the top card. Let Y be the number of cards you turn over until you observe the first red card.
The random variable Y has which of the following probability distributions?
A. the Normal distribution with mean 5
B. the binomial distribution with p = 0.5
C. the geometric distribution with probability of success 0.5
D. the uniform distribution that takes value 1 on the interval from 0 to 1
E. none of the above
26. A factory makes silicon chips for use in computers. It is known that about 90% of the chips meet specifications. Every
hour a sample of 18 chips is selected at random for testing and the number of chips that meet specifications is recorded.
What is the approximate mean and standard deviation of the number of chips meeting specifications?
A. = 1.62;  = 1.414
B. = 1.62;  = 1.265
C. = 16.2;  = 1.62
D. = 16.2;  = 1.273
E. = 16.2;  = 4.025