Clothing sizes are not standardized across brands. Suppose that a large study of women's size 10 jeans revealed that the mean hip measurment was 39.7 in with a standard deviation of 1.3 in. As part of a project for a fashion merchandizing class, Mallorie selects a simple random sample of 15 pairs of women's size 12 jeans and records the following hip measurements, in inches. 40.3,41.0,42.2,40.7,40.7,39.4,40.0,41.2,41.4,41.0,42.5,42.9,40.7,40.6,41.3 Mallorie plans to use this data to construct a 95% confidence interval for ?, the mean hip measurement of women's size 12 jeans. She assumes that the hip measurements are normally distributed and that the population standard deviation is 1.3 in. The sample mean, ?⎯⎯⎯, 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 12 jeans? Give your answer precise to two decimal places. What is the margin of error for Mallorie's confidence interval? Give your answer precise to two decimal places. Choose the correct interpretation of Mallorie's confidence interval. Mallorie is 95% sure that the mean hip measurement of size 12 jeans is between 40.51 in and 41.61 in. There is a 95% chance that the mean hip measurement of size 12 jeans falls between 40.40 in and 41.72 in. Mallorie is 95% sure that the mean hip measurement of size 12 jeans is between 40.40 in and 41.72 in. There is a 95% chance that the mean hip measurement of size 12 jeans falls between 40.51 in and 41.61 in. In 95% of all samples, the sample mean will fall between 40.40 in and 41.72 in.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Clothing sizes are not standardized across brands. Suppose that a large study of women's size 10 jeans revealed that the mean hip measurment was 39.7 in with a standard deviation of 1.3 in. As part of a project for a fashion merchandizing class, Mallorie selects a simple random sample of 15 pairs of women's size 12 jeans and records the following hip measurements, in inches.

40.3,41.0,42.2,40.7,40.7,39.4,40.0,41.2,41.4,41.0,42.5,42.9,40.7,40.6,41.3

Mallorie plans to use this data to construct a 95% confidence interval for ?, the mean hip measurement of women's size 12 jeans. She assumes that the hip measurements are normally distributed and that the population standard deviation is 1.3 in.

The sample mean, ?⎯⎯⎯, 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 12 jeans? Give your answer precise to two decimal places.

What is the margin of error for Mallorie's confidence interval? Give your answer precise to two decimal places.

Choose the correct interpretation of Mallorie's confidence interval.

Mallorie is 95% sure that the mean hip measurement of size 12 jeans is between 40.51 in and 41.61 in.

There is a 95% chance that the mean hip measurement of size 12 jeans falls between 40.40 in and 41.72 in.

Mallorie is 95% sure that the mean hip measurement of size 12 jeans is between 40.40 in and 41.72 in.

There is a 95% chance that the mean hip measurement of size 12 jeans falls between 40.51 in and 41.61 in.

In 95% of all samples, the sample mean will fall between 40.40 in and 41.72 in.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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