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. S627, 5617, S732, S735, $639, S569, S494, $566, S648, S767, S683, S604, S727, S896, S751, $616, S664, S516 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 a = 0.05 to test the null hypothesis, H: u = 704 against the alternative hypothesis, H:< 704, where u 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, x, 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. se s Next, compute the 1-statistic of the test. Report your answer with four decimals of precision. 1-statistic = Then, use software to calculate the P-value for the test. Report your answer with four decimals of precision. P-value =

Answer 1

solution from the given data 621+617732+--..+ 616+664 Sb 18 18 >> 53|658.39 »S E (: 33" N- (627-658-39) + (617-658.3917 ---...+(516-658.3912 18-1 then 16526.278 165 226 278 17 2) 9719. 1928 -) So 98.58597 > S = 18.591 >> test stak's hic Given,

Hoiu=r04 hai l 704 658.39-704 do 98.59118 Wie - 45.61 23.2379 >> t = -1.96277 >> P-value = 10.0331 z vera should make the decision to resect the noll hypothesis . The conclusion is that there is sufficient evidence that the mediam . salary mediam salary at women af women in sales and office the occupation sector is less than $104