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)?