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Suppose that a large study of women's size 6 jeans revealed that the mean hip measurement was 36.9 inches with a standard deviation of 0.8 inches.

Answer :

The mean hip measurement for the sample of size 8 jeans is 38.16 inches. The margin of error for Mallorie's 99% confidence interval is approximately 0.53 inches, leading to a range of 37.66 inches to 38.73 inches for the mean hip measurement.

To find the mean hip measurement [tex](\( \bar{x} \))[/tex] for the random sample of 15 pairs of women's size 8 jeans, we calculate the average of the given hip measurements:

[tex]\[ \bar{x} = \frac{{39.1 + 38.7 + \dots + 38.6}}{{15}} \][/tex]

[tex]\[ \bar{x} = \frac{{572.4}}{{15}} \][/tex]

[tex]\[ \bar{x} = 38.16 \text{ inches} \][/tex]

The mean hip measurement for the random sample of 15 pairs of women's size 8 jeans is 38.16 inches.

Now, to find the margin of error (ME) for Mallorie's confidence interval, we use the formula:

[tex]\[ ME = Z \times \frac{{\sigma}}{{\sqrt{n}}} \][/tex]

Given:

- Confidence level: 99% corresponds to a Z-score of approximately 2.576

- Population standard deviation [tex](\( \sigma \))[/tex]: 0.8 inches

- Sample size ( n ): 15

[tex]\[ ME = 2.576 \times \frac{{0.8}}{{\sqrt{15}}} \][/tex]

[tex]\[ ME = 2.576 \times \frac{{0.8}}{{3.87298}} \][/tex]

ME = 0.533

The margin of error for Mallorie's confidence interval is approximately 0.53 inches.

The correct interpretation of Mallorie's confidence interval is: "Mallorie is 99% sure that the mean hip measurement of size 8 jeans is between 37.66 inches and 38.73 inches."

Complete Question:

Clothing sizes are not standardized across brands. Suppose that a large study of women's size 6 jeans revealed that the mean hip measurment was 36.9 in with a standard deviation of 0.8 in. As part of a project for a fashion merchandizing class, Mallorie selects a simple random sample of 15 pairs of women's size 8 jeans and records the following hip measurements, in inches 39.1 38.7,38.7,37.7,38.0, 37.2, 38.1,38.2, 37.5, 37.3, 38.9, 37.8, 38.6, 38.5,38.6 Mallorie plans to use this data to construct a 99% confidence interval for w, the mean hip measurement of women's size 8 jeans. She assumes that the hip measurements are normally distributed and that the population standard deviation is 0.8 in. The sample mean, I, 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 8 jeans? Give your answer precise to two decimal places. in What is the margin of error for Mallorie's confidence interval? Give your answer precise to two decimal places. ma in Choose the correct interpretation of Mallorie's confidence interval. Mallorie is 99% sure that the mean hip measurement of size 8 jeans is between 37.71 in and 38.67 in. There is a 99% chance that the mean hip measurement of size 8 jeans falls between 37.71 in and 38.67 in. Mallorie is 99% sure that the mean hip measurement of size 8 jeans is between 37.66 in and 38.73 in. There is a 99% chance that the mean hip measurement of size 8 jeans falls between 37.66 in and 38.73 in. In 99% of all samples, the sample mean will fall between 37.66 in and 38.73 in.

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