Question

Clothing sizes are not standardized across brands. Suppose that a large study of women's size 14 jeans revealed that the mean hip measurment was 42.3 in with a standard deviation of 1.2 in. As part of a project for a fashion merchandizing class, Mallorie selects a simple random sample of 15 pairs of women's size 16 jeans and records the following hip measurements. in inches. 44.5,43.0, 46.6, 42.9.43.7.43.9.42.4, 43.2, 43.1.44.4.46.1, 44.7,44.4, 43.9,44.7 Mallorie plans to use this data to construct a 99% confidence interval for fe, the mean hip measurement of women's size 16 jeans. She assumes that the hip measurements are normally distributed and that the population standard deviation is 1.2 in. The sample mean, x, is the point estimate for a confidence interval to estimate a population mean. What is the mean hip measurement for the random sample of 15 pairs of women's size 16 jeans? What is the margin of error for Mallorie's confidence interval? Choose the correct interpretation of Mallorie's confidence interval. a. Mallorie is 99% sure that the mean hip measurement of size 8 jeans is between 37.71 in and 38.67 in. b. In 99% of all samples, the sample mean will fall between 37.66 in and 38.73 in. c. There is a 99% chance that the mean hip measurement of size 8 jeans falls between 37.71 in and 38.67 in. d. There is a 99% chance that the mean hip measurement of size 8 jeans falls between 37.66 in and 38.73 in. e. Mallorie is 99% sure that the mean hip measurement of size 8 jeans is between 37.66 in and 38.73 in.

Answer 1

Using the z-distribution, we have that:

• The mean hip measurement for the random sample of 15 pairs of women's size 16 jeans is of 44.1 inches.

• The margin of error is of 0.8 in.

• The interpretation is: Mallorie is 99% sure that the mean hip measurement of size 16 jeans is between 43.3 in and 44.9 in.

The first step to solve this question, before building the confidence interval, is finding the sample mean, which is the sum of all observations divided by the number of observations. Hence:

$\overline{x} = \frac{44.5+43.0+46.6+42.9+43.7+43.9+42.4+43.2+43.1+44.4+46.1+44.7+44.4+43.9+44.7}{15} = 44.1$

The margin of error of a z-confidence interval is given by:

$M = z\frac{\sigma}{\sqrt{n}}$

In which:

• z is the critical value.
• $\sigma$ is the population standard deviation.
• n is the sample size.

We have to find the critical value, which is z with a p-value of $\frac{1 + \alpha}{2}$, in which $\alpha$ is the confidence level.

In this problem, $\alpha = 0.99$, thus, z with a p-value of $\frac{1 + 0.99}{2} = 0.995$, which means that it is z = 2.575.

Then, the margin of error is:

$M = z\frac{\sigma}{\sqrt{n}}$

$M = 2.575\frac{1.2}{\sqrt{15}}$

$M = 0.8$

The margin of error is of 0.8 in.

The interval is:

$\overline{x} \pm M$

$\overline{x} - M = 44.1 - 0.8 = 43.3$

$\overline{x} + M = 44.1 + 0.8 = 44.9$

The interpretation is:

Mallorie is 99% sure that the mean hip measurement of size 16 jeans is between 43.3 in and 44.9 in.

A similar problem is given at brainly.com/question/25300297