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1. An opinion poll asks a random sample of adults whether they favor banning ownership of
handguns by private citizens. A commentator believes that more than half of all adults favor
such a ban. The null and alternative hypotheses you would use to test this claim are
(a) H 0 : pö  0.5; H a : pö  0.5
(b) H 0 : pö  0.5; H a : pö  0.5
(c) H 0 : p  0.5; H a : p  0.5
(d) H 0 : p  0; H a : p  0
(e) None of the above. The answer is _Ho: p = 0.5, Ha: p > 0.5_____.
2. 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 advocate 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
H0:  = 14, Ha:  < 14
To do this, he selects 16 bags of this brand at random and determines the net weight of each.
He finds the sample mean to be x = 13.82 and the sample standard deviation to be s = 0.24.
We conclude that we would
(a) reject H0 at significance level 0.10 but not at 0.05.
(b) reject H0 at significance level 0.05 but not at 0.025.
(c) reject H0 at significance level 0.025 but not at 0.01.
(d) reject H0 at significance level 0.01.
(e) fail to reject H0 at the  = 0.10 level.
3. A Type I error in the previous question 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
4. You are thinking of using a t procedure to test hypotheses about the mean of a population using
a significance level of 0.05. You suspect that the distribution of the population is not Normal
and may be moderately skewed. Which of the following statements is correct?
(a) You should not use the t procedure because the population does not have a Normal
distribution.
(b) You may use the t procedure if your sample size is large, say, at least 50.
(c) You may use the t procedure, but you should probably claim only that the significance level
is 0.10.
(d) You may not use the t procedure. The t procedures are robust to non-Normality for
confidence intervals but not for tests of hypotheses.
(e) You may use the t procedure if there are no outliers.
5. After once again losing a football game to the archrival, a college’s alumni association
conducted a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni
from the population of all living alumni was taken. 64 of the alumni in the sample were in favor
of firing the coach. Suppose you wish to see if a majority of living alumni are in favor of firing
the coach. The appropriate test statistic is
(a) z  (0.64  0.5) (0.64)(0.36) 100
(b) z  (0.64  0.5)
(0.5)(0.5) 100
(c) z  (0.64  0.5)
(0.64)(0.36) 64
(d) z  (0.64  0.5)
(0.5)(0.5) 64
(e) t  (0.64  0.5)
(0.5)(0.64) 100
6. We prefer the t procedures to the z procedures for inference about a population mean because
(a) z can be used only for large samples.
(b) z requires that you know the population standard deviation  .
(c) z requires that you can regard your data as an SRS from the population of interest.
(d) z requires that your population be Normally distributed.
(e) z requires that your observations be independent.
7. Looking online (for example, at espn.go.com) you find the salaries of all 22 players for the
Chicago Cubs as of opening day of the 2005 baseball season. The club total was $87 million,
eighth in the major leagues. Which inference procedure would you use to estimate the
average salary of the Cubs players?
(a) one-sample z interval for 
(b) one-sample t interval for 
(c) one-sample t test
(d) one-sample z test
(e) none of these
8. You read in the report of a psychology experiment that “separate analyses for our two groups
of 12 participants revealed no overall placebo effect for our student group (mean = 0.08, SD
= 0.37,
t(11) = 0.49) and a significant effect for our non-student group (mean = 0.35, SD = 0.37,
t(11) = 3.28, p < 0.01).” Are the two values given for the t test statistic correct? (The null
hypothesis is that the mean effect is zero.)
(a) Yes, both are correct.
(b) The t statistic for the student group is correct, but the one for the non-student group is
incorrect.
(c) The t statistic for the non-student group is correct, but the one for the student group is
incorrect.
(d) Both t statistics are incorrect.
(e) We can’t tell whether either t statistic is correct, because we aren’t given the actual data.
9. The water diet requires one to drink two cups of water every half hour from when one gets up
until one goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers
agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the
diet. The weights (in pounds) are
Person
Weight before the diet
Weight after six weeks
1
180
170
2
125
130
3
240
215
4__
150
152
For the population of all adults, assume that the weight loss after six weeks on the diet (weight
before beginning the diet – weight after six weeks on the diet) is Normally distributed with
mean µ. To determine if the diet leads to weight loss, we test the hypotheses
H0:  = 0, Ha:  > 0
Based on these data we conclude that
(a) we would not reject H0 at significance level 0.10.
(b) we would reject H0 at significance level 0.10 but not at 0.05.
(c) we would reject H0 at significance level 0.05 but not at 0.01.
(d) we would reject H0 at significance level 0.01.
(e) the sample size is too small to allow use of the t procedures.
10. Because t procedures are robust, the most important condition for their use is
(a) the population standard deviation is known
(b) the population distribution is exactly Normal
(c) the data can be regarded as an SRS from the population
(d) np and n(1 – p) are both at least 10
(e) there are no outliers in the sample data
11. Which of the following 95% confidence intervals would lead us to reject H 0 : p  0.30 in
favor of H a : p  0.30 at the 5% significance level?
(a) (0.30, 0.38)
(b) (0.19, 0.27)
(c) (0.27, 0.31)
(d) (0.24, 0.30)
(e) None of these
12. A medical researcher wishes to investigate the effectiveness of exercise versus diet in losing
weight. Two groups of 25 overweight adult subjects are used, with a subject in each group
matched to a similar subject in the other group on the basis of a number of physiological
variables. One of the groups is placed on a regular program of vigorous exercise but with no
restriction on diet, and the other is placed on a strict diet but with no requirement to exercise.
The weight losses after 20 weeks are determined for each subject, and the difference between
matched pairs of subjects (weight loss of subject in exercise group  weight loss of matched
subject in diet group) is computed. The mean of these differences in weight loss is found to
be  2 lb with standard deviation s = 4 lb. Is this evidence of a difference in mean weight loss
for the two methods? To answer this question, you should use
(a) one-proportion z test
(b) one-sample t test
(c) one-sample z test
(d) one-proportion z interval
(e) one-sample t interval
13. A random sample of 100 voters in a community produced 59 voters in favor of Candidate A.
The observed value of the test statistic for testing the null hypothesis H 0 : p  0.5 versus the
alternative hypothesis H a : p  0.5 is
(a) z   0.59  0.5
(c) t   0.59  0.5
(b) z   0.59  0.5
(0.59)(0.41) 100 
(0.59)(0.41) 100 
(d) t   0.59  0.5
(0.5)(0.5) 100 
(0.5)(0.5) 100 
(e) None of these
14. A noted psychic was tested for ESP. The psychic was presented with 200 cards face down
and asked to determine if the card was one of five symbols: a star, cross, circle, square, or
three wavy lines. The psychic was correct in 50 cases. Let p represent the probability that the
psychic correctly identifies the symbol on the card in a random trial. Assume the 200 trials
can be treated as an SRS from the population of all guesses the psychic would make in his
lifetime. Which inference procedure would you use to determine whether the psychic is
doing better than just guessing?
(a) one-proportion z test
(b) one-sample t test
(c) one-sample z test
(d) one-proportion z interval
(e) one-sample t interval
Different varieties of fruits and vegetables have different amounts of nutrients. These differences
are important when these products are used to make baby food. We wish to compare the
carbohydrate content of two varieties of peaches. The data were analyzed with SAS, and the
following output was obtained:
VARIETY
1
2
VARIANCES
UNEQUAL
EQUAL
N
5
7
MEAN STD DEV STD ERROR
33.6
3.781
1.691
25.0 10.392
3.927
T
2.0110
1.7490
MIN
29.000
2.000
MAX
38.000
33.000
DF PROB > |T|
8.0
0.0791
10.0
0.1109
15. We wish to test if the two varieties are significantly different in their mean carbohydrate
content. The null and alternative hypotheses are
(a) H 0 : 1   2 ; H a : 1   2
(b) H 0 : 1   2 ; H a : 1   2
(c) H 0 : 1   2 ; H a : 1   2
(d) H 0 : x1  x2 ; H a : x1  x2
(e) H 0 : x1  x2 ; H a : x1  x2
16. The test statistic and P-value are
(a) 1.7490; 0.0318
(b) 1.7490; 0.0554
(c) 2.0110; 0.1582
(d) 2.0110; 0.0791
(e) 2.0110; 0.0396
17. Thirty-five people from a random sample of 125 workers from Company A admitted to using
sick leave when they weren’t really ill. Seventeen employees from a random sample of 68
workers from Company B admitted that they had used sick leave when they weren’t ill. A
95% confidence interval for the difference in the proportions of workers at the two
companies who would admit to using sick leave when they weren’t ill is
(0.28)(0.72) (0.25)(0.75)
(a) 0.03 

125
68
(0.28)(0.72) (0.25)(0.75)

125
68
(0.28)(0.72) (0.25)(0.75)
(c) 0.03  1.645

125
68
(b) 0.03  1.96
1
 1
(d) 0.03  1.96 
 0.2690.731
 125 68 
1
 1
(e) 0.03  1.645 
 0.2690.731
 125 68 
18. Popular wisdom is that eating presweetened cereal tends to increase the number of dental
caries (cavities) in children. A sample of children was (with parental consent) entered into a
study and followed for several years. Each child was classified as a sweetened-cereal lover or
a nonsweetened cereal lover. At the end of the study, the amount of tooth damage was
measured. Here are the summary data:
Group
n
Mean
Std. Dev
Sugar bombed
No sugar
10
15
6.41
5.20
5.0
15.0
An approximate 95% confidence interval for the difference in the mean tooth damage is
(a) 6.41  5.20 2.26
5 15

10 15
(c)
(e) 6.41  5.20 1.96
25 225

100 225
(b) 6.41  5.20 2.26
25 225

10 15
(d) 6.41  5.20 2.26
25 225

100 225
19. The power takeoff driveline on tractors used in agriculture is a potentially serious hazard to
operators of farm equipment. The driveline is covered by a shield in new tractors, but for a
variety of reasons, the shield is often missing on older tractors. Two types of shields are the
bolt-on and the flip-up. It was believed that the bolt-on shield was perceived as a nuisance by
the operators and deliberately removed, but the flip-up shield is easily lifted for inspection and
maintenance and may be left in place. In a study initiated by the U.S. National Safety Council, a
sample of older tractors with both types of shields was taken to see what proportion were
removed. Of 183 tractors designed to have bolt-on shields, 35 had been removed. Of the 136
tractors with flip-up shields, 15 were removed. We wish to test the hypothesis H0: pb = pf vs. Ha:
pb  pf where pb and pf are the proportion of tractors with the bolt-on and flip-up shields
removed, respectively. Which of the following conditions for performing the appropriate
significance test is satisfied in this case?
(a) Both population distributions are Normally distributed.
(b) Two independent simple random samples were chosen.
(c) Both sample sizes are at least 30.
(d) np and n(1 – p) are both large enough to use Normal calculations.
(e) The sample size is at least 10 times the population size.
20. An SRS of size 100 is taken from a population having proportion 0.8 successes. An
independent SRS of size 400 is taken from a population having proportion 0.5 successes.
The sampling distribution for the difference in sample proportions has what standard
deviation?
(a) 1.3
(b) 0.40
(c) 0.047
(d) 0.0002
(e) None of the above. The answer is _____________________________.