1) In a study designed to test the effectiveness of acupuncture for treating migraine,
100 patients were randomly selected and treated with acupuncture. After onemonth treatment, the number of migraine attacks for the group had a mean of 2
and standard deviation of 1.5. Construct a 90% confidence interval estimate of
the mean number of migraine attacks for people treated with acupuncture.
2) Sara conducted a survey on a random sample of 100 adults. 58 adults in the
sample chose banana as his / her favorite fruit. Construct a 95% confidence
interval estimate of the proportion of adults whose favorite fruit is banana.
3) A researcher claims the proportion of auto accidents that involve teenage drivers
is greater than 15%. ABC Insurance Company checks police records on 300
randomly selected auto accidents and notes that teenagers were at the wheel in
50 of them. Assume the company wants to use a 0.05 significance level to test
the researcher’s claim.
(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic.
(c) Determine the P-value for this test.
(d) Is there sufficient evidence to support the claim that the proportion of auto
accidents that involve teenage drivers is greater than 15%? Explain. 4) In a study of memory recall, 5 people were given 10 minutes to memorize a list of
20 words. Each was asked to list as many of the words as he or she could
remember both 1 hour and 24 hours later. The result is shown in the following
table.
Subject
1
2
3
4
5 1 hour
24 hours
later
later
14
12
18
17
11
9
15
13
12
12 Is there evidence to suggest that the mean number of words recalled after 1 hour
exceeds the mean recall after 24 hours? Assume we want to use a 0.05 significance
level to test the claim.
a (a) Identify the null hypothesis and the alternative hypothesis.
b (b) Determine the test statistic.
c (c) Determine the P-value. d (d) Is there sufficient evidence to support the claim that the mean number of
words recalled after 1 hour exceeds the mean recall after 24 hours? Justify your
conclusion.
5) A toy store sells five different types of teddy bears. The manager reports that the
five types are equally popular. Suppose that a sample of 500 purchases yields
observed counts of 105, 85, 105, 95, and 110 for types 1, 2, 3, 4, and 5,
respectively.
Type
Numbe
r 1 2 105 85 3
10
5 4
95 5
11
0 Assume we want to use a 0.05 significance level to test the claim that the four types are
equally popular.
(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic.
(c) Determine the P-value.
(d) Is there sufficient evidence to support the manager’s claim that the five types are
equally popular? Justify your answer. 6) A professor believes that the average quiz score is a good predictor of final
score. A random sample of 10 students produced the following data where x is
the average quiz score and y is the final score.
x
y 73
70 93
96 45
50 65
70 100
94 40
38 85
83 70
65 75
77 (a) Find an equation of the least squares regression line.
(b) Based on the equation from part (a), what is the predicted final exam score if the
average quiz score is 80? 7) A study of 8 different weight loss programs involved 200 subjects. Each of the 8
programs had 25 subjects in it. The subjects were followed for 12 months. Weight
change for each subject was recorded. We want to test the claim that the mean
weight loss is the same for the 8 programs.
a (a)
Complete the following ANOVA table with sum of squares, degrees of
freedom, and mean square
Source of
Sum of
Degrees of
Mean 85
87 Variation
Factor
(Between)
Error (Within)
Total Squares Freedom Square 65.4
653.05 199 N/A a (b) Determine the test statistic.
b (c) Determine the P-value.
c (d) Is there sufficient evidence to support the claim that the mean weight loss is
the same for the 8 programs at the significance level of 0.05? Explain.
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