Question

Clothing sizes are not standardized across brands. Suppose that a large study of women's size 8 jeans revealed that the mean hip measurement was 38.1 in with a standard deviation of 1.0 in. As part of a project for a fashion merchandizing class, Mallorie selects a simple random sample of 15 pairs of women's size 10 jeans and records the following hip measurements, in inches.

40.1 , 39.6 , 39.1 , 40.5 , 39.3 , 38.4 , 40.3 , 40.8 , 39.7 , 40.0 , 40.9 , 40.1 , 39.5 , 38.5 , 39.5

Mallorie plans to use this data to construct a 95% confidence interval for μ , the mean hip measurement of women's size 10 jeans. She assumes that the hip measurements are normally distributed and that the population standard deviation is 1.0 in. The sample mean is the point estimate for a confidence interval to estimate a population mean.

a) What is the mean hip measurement for the random sample of 15 pairs of women's size 10 jeans? Give your answer precise to two decimal places.
b) What is the margin of error for Mallorie's confidence interval? Give your answer precise to two decimal places.
c) Choose the correct interpretation of Mallorie's confidence interval:

Mallorie is 95% sure that the mean hip measurement of size 10 jeans is between 39.33 in and 40.18 in.

Mallorie is 95% sure that the mean hip measurement of size 10 jeans is between 39.24 in and 40.26 in.

There is a 95% chance that the mean hip measurement of size 10 jeans falls between 39.24 in and 40.26 in.

There is a 95% chance that the mean hip measurement of size 10 jeans falls between 39.33 in and 40.18 in.

In 95% of all samples, the sample mean will fall between 39.24 in and 40.26 in.

Answer 1

a) The sample size n = 15

The mean hip measurement for the random sample of 15 pairs of women's size 10 jeans is

b) Degree of Freedom = n - 1 = 15 - 1 = 14. It is given that the population standard deviation

Therefore, at 95% confidence , the critical value of the standard normal variate is .

Therefore, the margin of error is

The confidence interval for the population mean is c) There is a 95% chance that the mean hip measurement of size 10 jeans falls between 39.24 in and 40.26 in.