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=

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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