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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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