2-Population Procedures Review
AP Statistics
Name:_____________________________
I. Multiple Choice
1. A survey of 1,000 Americans reveals that 525 believe that whales are an endangered animal and should have
protection from the fishing industry. In a survey of 750 Japanese, 325 believe that whales are endangered and
should be protected. To test at the 5 percent significance level whether or not the data are significant evidence
that the proportion of Japanese who believe that whales need protection is less than the proportion of Americans
with this belief, a student sets up the following: 𝐻0 : 𝑝 = .525 and 𝐻𝑎 : 𝑝 < .525, where p is the proportion of
Japanese who believe that whales need protection. Which of the following is a true statement?
(a) The student has set up a correct hypothesis test.
(b) Given the large sample sizes, a 1 percent significance level would be more appropriate.
(c) A two-sided test would be more appropriate.
525+325
(d) Given that 1000+750 = .486, 𝐻𝑎 : 𝑝 < .486 would be more appropriate.
(e) A two-population difference in proportions hypothesis test would be more appropriate.
2. Should there be more restrictions on handguns? In a 1995 pre-Columbine survey, 255 out of 1,020 adults
answered in the affirmative; in a 2000 post-Columbine survey, 352 out of 1,100 answered affirmatively.
Establish a 90 percent confidence interval estimate of the difference between the proportions of adults in 1995
and 2000 who support more restrictions on handguns.
(.25)(.75)
(a) (. 25 − .32) ± 1.645√
(b) (. 25 − .32) ± 1.645 (
1,020
(.25)(.75)
√1,020
(.25)(.75)
(c) (. 25 − .32) ± 1.96√
(d) (. 25 − .32) ± 1.96 (
1,020
(.25)(.75)
√1,020
+
+
+
+
√(.25)(.75)
(e) (. 25 − .32) ± 2.576 (
1,020
(.32)(.68)
1,100
(.32)(.68)
√1,100
)
(.32)(.68)
1,100
(.32)(.68)
√1,100
+
)
√(.32)(.68)
1,100
)
3. An anthropologist believes that human skull sizes increased between two time periods. He plans to
randomly sample 30 skulls from each period and will reject any equality claim if the mean skull circumference
in the second time period sample is at least 1 inch greater than the mean circumference from the first period
sample. If the standard deviation of skull circumferences in all time periods is known to be 2.3 inches, what is
the probability the anthropologist will mistakenly reject a correct null hypothesis of equality?
(a) .009
(b) .023
(c) .046
(d) .594
(e) There is insufficient information given to calculate this probability.
4. An HR executive wishes to know the difference in job satisfaction rating (on a standard satisfaction test)
between employees who exercise regularly and those who don’t. Suppose the standard deviation of each group
is known to be 4.5. How large a sample (same number) from each group should be interviewed if the executive
wishes to be 90 percent certain of knowing the difference in ratings to within 1 point?
(a) 10
(b) 55
(c) 110
(d) 156
(e) 202
5. In a random survey of 500 women, 315 said they would rather be poor and thin than rich and fat; in a
random survey of 400 men, 220 said they would rather be poor and thin than rich and fat. Is there sufficient
evidence to show that the proportion of women who would rather be poor and thin than rich and fat is greater
than the proportion of men who would rather be poor and thin than rich and fat?
(a) Because .63 > .55 there is strong evidence that the proportion of women is greater than that of men.
(b) Because .0075 < .01 there is very strong evidence that the proportion of women is greater than that of
men.
(c) Because .01 < .0329 < .05 there is strong evidence that the proportion of women is greater than that of
men.
(d) There is insufficient evidence that the proportion of women is greater than that of men.
(e) There is insufficient evidence to determine whether the proportion of women is greater than that of men.
6. Before televised debates, a poll of 800 registered voters showed 560 in favor of a particular candidate; after
the debates a poll of 600 voters showed 450 in favor of the candidate. Is there sufficient evidence that the
candidate’s popularity has increased—what is the test statistic?
.7−.75
(a) 𝑧 =
(.7)(1−.7) (.75)(1−.75)
+
800
600
√
.7−.75
(b) 𝑧 =
√(.7214)(1−.7214)+(
(c) 𝑧 =
(d) 𝑧 =
1
1
+ )
800 600
.7−.75
√800(.7)(1−.7)+600(.75)(1−.75)
.7−.75
(.725)(1−.725)
700
√
(e) 𝑧 =
.7−.75
√700(.725)(1−.725)
7. Two pain relief medicines are tested on random samples of post-operative patients at the 5 percent
significance level as to whether or not mean durations of relief are different. The data give:
Brand
A
B
Sample Size
20
15
Mean Relief (min)
131
140
Standard Deviation (min)
12
15
What is the conclusion of a two-sample t-test?
(a)
(b)
(c)
(d)
(e)
p-value < .05 so reject 𝐻0
p-value < .05 so fail to reject 𝐻0
p-value > .05 so reject 𝐻0
p-value > .05 so fail to reject 𝐻0
The 5 percent significance level is inappropriate for medical decisions.
Answers: 1. E, 2. A, 3. C, 4. C, 5. B, 6. B, 7. D
II. Free Response
8. Men and women were surveyed as to the ideal number of children a family should have. For 500 men, the
mean was 2.95 with a standard deviation of 1.65; for 450 women, the mean was 3.05 with a standard deviation
of 1.80. Assuming all assumptions are met, establish a 90 percent confidence interval for the difference in
population means.
9. North Carolina State University looked at the factors that affect the success of students in a required
chemical engineering course. Students must get a C or better in the course in order to continue as chemical
engineering majors. There were 65 students from urban or suburban backgrounds, and 52 of these students
succeeded. Another 55 students were from rural or small-town backgrounds; 30 of these students succeeded in
the course. Give a 95% confidence interval for the size of the difference.
10. A random sampling of 150 sales at each of two used-car dealerships notes the numbers of cars sold at
various prices:
Dealership
A
B
$5,000 $10,000 $15,000 $20,000
12
48
78
12
29
57
41
23
Mean
$13,000
$11,933
(a) Is the observed difference in means significant?
(b) Is the observed difference in proportions of cars sold for $20,000 significant?
SD
$3,754
$4,839