Statistics 101
Exam 4
May 10, 2002
Name:
ID#
INSTRUCTIONS: Read the questions carefully and completely. Answer each question and show
work in the space provided. Partial credit will not be given if work is not shown. When asked to
explain, describe, or comment, do so within the context of the problem.
1. [15 pts] Does regular exercise lead to lower resting pulse rates? A random sample of 20 college
students was selected. Each student was asked whether or not they exercised regularly (at
least 30 minutes of aerobic exercise 3 times a week). The resting pulse rate for each student
was also taken. Below are the summarized data.
Number
Mean
Std. Dev.
No regular
Exercise
8
72.0
9.13
Regular
Exercise
12
65.0
7.01
(a) [4] Is this an observational study or an experiment? Explain briefly.
(b) [11] Determine whether the mean resting pulse rate for college students who exercise
regularly is lower than that of college students who do not exercise regularly. Be sure to
include all the steps of a test of hypothesis.
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2. [18 pts] For each of the following indicate: (1) whether it is an observational study or an
experiment, (2) what statistical method you would use: two sample or matched pair and (3)
the formula you would use.
(a) [6] A pretest is given to students to assess their knowledge of the frog’s anatomy prior
to covering this topic in class. The teacher wishes to see if boys are different from girls
in terms of their mean pretest score.
(b) [6] Students are then assigned at random to two groups. One group of students do
simulated frog dissection using a computer program. The other group dissects actual
frogs. A posttest on the frog’s anatomy is given after the dissection. The teacher wishes
to estimate the difference in mean posttest scores for the two groups.
(c) [6] The teacher also wants to see if students who did the computer dissection have a
higher mean score on the posttest when compared to the pretest.
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3. [15 pts] A business woman owns two fast food franchises in the same town. She wants to
compare the average daily sales of the two. She chooses 5 days at random. On each day she
records the daily sales for each franchise. Below are the data.
Day
Franchise 1
Franchise 2
Difference
1
1112
996
116
2
1212
1238
−26
3
1481
1385
96
4
2017
1867
150
5
2406
2212
194
Std. Dev.
551.4
492.4
82.6
(a) [3] Explain why this is a matched pairs problem.
(b) [5] Construct a 95% confidence interval for the mean difference in franchise daily sales.
(c) [4] Based on the confidence interval in (b), do the two franchises differ in terms of mean
daily sales? Explain briefly.
(d) [3] What conditions should be satisfied in order for the procedure in (b) to be valid?
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4. [22 pts] The 1996 General Social Survey obtained information on religious preference and
opinion on when premarital sex might be wrong. Below are the data.
Religious
Preference
Catholic
Protestant
Other
None
When is premarital sex wrong?
Almost
Never Sometimes Always Always
226
120
37
62
384
227
117
355
74
37
16
15
147
45
13
20
831
429
183
452
Total
445
1083
142
225
1895
(a) [3] What proportion of the entire sample feels premarital sex is always wrong? (round
your answer to 3 decimal places).
(b) [4] Construct a 95% confidence interval for the proportion of the population that feels
premarital sex is always wrong.
(c) [3] Among only Catholics, what proportion feel premarital sex is always wrong? (round
your answer to 3 decimal places).
(d) [3] If religious preference and opinion on when premarital sex might be wrong are independent, what is the expected number of Catholics who feel premarital sex is always
wrong?
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(e) [3] What is the contribution to the χ 2 test statistic for the cell Catholic and feel premarital sex is always wrong?
(f) [1] How many degrees of freedom will be associated with the χ 2 test statistic?
(g) [3] The value of the χ2 test statistic is 147.0 with an associated P-value < 0.0001. What
does indicate about the independence of religious preference and opinion on when premarital sex is wrong?
(h) [2] Based on this survey, does religious preference cause people to hold a particular
opinion on when premarital sex is wrong? Explain briefly.
5. [5 pts] You are planning a survey and want to determine how many people to sample.
(a) [3] If you want to estimate a population proportion and have a maximum margin of
error of 2.2%, how many people should you have in your sample?
(b) [2] Once you get your sample you discover you have 948 males in it. What is the
maximum margin of error for estimating the male population proportion?
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