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Marketing and Consumer Behavior
The owner of a small tailoring shop keeps careful records of all alterations. Two common alterations to men's clothing are lengthening the inseam on pants and letting out a sports coat around the waist. A random sample of each type of alteration was obtained, and the summary statistics are given in the table below. Measurements are in inches.
Alteration
Sample size
Sample mean
Assumed
Pants inseam
33
0.74
0.22
Sports coat waist
42
1.05
0.37
a. Find a 95% confidence interval for the mean alteration of the inseams on men's pants.
b. How large a sample is necessary for the bound on the error of estimation to be 0.05 for the confidence interval in part (a)?
c. Find a 90% confidence interval for the mean alteration of the waists of sports coats.
d. How large a sample is necessary for the bound on the error of estimation to be 0.07 for the confidence interval in part (c)?
For this table, the value of the chi-square statistic is 5.34, and the corresponding p-value is .02. Based on these results, state a conclusion about the two variables and explain how you came to this conclusion.
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