1. A pharmaceutical firm is interested in the efficacy of a new drug and of a standard
drug. The research division of the firm randomly selects two groups of volunteers. One
group is given the new drug and the other group is given the standard drug. Data are
recorded on the effects of each drug. Is the research division using dependent or
independent samples? Why?
2. First National Bank and City National Bank are competing for customers who would
like to open IRAs (individual retirement accounts). Thirty-two weeks are randomly
selected for First National Bank and another 32 weeks are randomly selected for City
National. The total amount deposited into IRAs is noted for each week. A summary of
data (deposits in thousands of dollards) from the survey is as follows. First National 𝑋̅1 =
4.1, 𝜎1 = 1.2. City National: 𝑋̅2 = 3.5, 𝜎2 = 0.9. Use a 98% confidence interval to
estimate the difference in the mean weekly deposits into IRAs for each bank.
3. A production manager wishes to determine if there is a difference in the number of
production units produced by the night shift and the day shift. A random sample of night
and day shifts is selected, and the number of production units for each shift is recorded.
The following statistics resulted.
Day Shift
Night Shift
𝑋̅
27.4
18.3
𝜎
6.4
5.9
𝑛
60
60
a. Find a 90% confidence interval on the difference in the mean number of
production units for the two shifts.
b. Calculate a 99% confidence interval for part a.
c. Compare the two confidence intervals in parts a and b, and comment on the length
of the intervals.
4. Advertisers examine the average age of viewers of TV programs. For example 60
Minutes reportedly has one of the highest average ages at 57. Suppose that a marketing
analyst believes that the age gap between 60 Minutes and Star Trek: Voyager has
narrowed to less than the historical 15 years. A random sample of 100 viewers from each
of the TV programs was selected and the results are as follows.
Sample mean
Population standard deviation
Sample size
60 Minutes
55.6
10.8
100
Star Trek: Voyager
41.8
7.9
100
a. Construct a 99% confidence interval on the difference of the average ages for the
viewers of the two TV programs. How can you interpret this interval?
b. Test the hypothesis that the difference in the average age of viewers for these two
programs is less than 15 years. Use a significance level of 1%.
c. Why can you not use the confidence interval in part a to test the hypothesis in part
b?
5. A market research analyst suspects that the average monthly household expenditure
for long distance telephone service in City A exceeds the average monthly household
expenditure for long distance telephone service in City B by more than $20. The
market research analyst believes that monthly household expenditures for long
distance telephone service are normally distributed both in City A and City B, and that
the two population variances are equal. The market research analyst took a random
sample of 12 City A households and a random sample of 15 City B households and
recorded the following information regarding their monthly expenditures for long
distance telephone service.
Mean
Std. Dev.
Sample Size
City A
City B
83
18
12
54
12
15
If a 99% confidence interval for the mean difference between average monthly household
expenditure for long distance telephone service in City A and the average monthly
expenditure in City B extends from X to Y, what is the value of X?