Answered: ording to the Bureau of Labor…

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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Question

Suppose that Vera wants to test the hypothesis that women make less money than men doing the same job. According to the Bureau of Labor Statistics (BLS), the median weekly earnings for men in the sales and office occupation sector in 2015 was $704. Vera collected median weekly earnings data for women in 2015 from a random subset of 18 positions in the sales and office occupation sector. The following is the sample data.

$627, $617, $732, $735, $639, $569, $494, $566, $648, $767, $683, $604, $727, $896, $751, $616, $664, $516

Vera assumes that the women's median weekly earnings data is normally distributed, so she decides to perform a t-test at a significance level of α = 0.05 to test the null hypothesis, ?0:?=704 against the alternative hypothesis, ?1:?<704, where ? is the population mean.

If the requirements for performing a t-test have not been met, only answer the final question. Otherwise, answer all five of the following questions.

First, compute the mean, ?⎯⎯⎯, of Vera's sample. Report your answer with two decimals of precision.

?⎯⎯⎯= $

Then, compute the sample standard deviation, s. Report your answer with two decimals of precision.

?= $

Next, compute the t-statistic of the test. Report your answer with four decimals of precision.

?-statistic=

Then, use software to calculate the ?-value for the test. Report your answer with four decimals of precision.

?-value=

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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