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 16 positions in the sales and office occupation sector. The following is the sample data.

• $566, $648, $767, $683, $604, $727, $751, $614, $664, $516, $675, $467, $680, $655, $638, $627

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, H0:μ=704 against the alternative hypothesis, H1:μ<704 , where  μ 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.

x¯=  $

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

s=  $

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

t-statistic=

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

P-value=

Finally, use the words and descriptions below to state the decision and conclusion of Vera's test.

Vera                decision

the                . The conclusion is that               

the median salary of women in the sales and office occupation sector

                .

Answer Bank

to reject

alternative hypothesis

should make the

there is sufficient evidence that

is greater than $704

is equal to $704

is less than $704

about

cannot make a

because the requirements have not been met

no conclusion can be made about

null hypothesis

to fail to reject

there is insufficient evidence that

Adapted from: Bureau of Labor Statistics. Median weekly earnings of full-time wage and salary workers by detailed occupation and sex. http://www.bls.gov/cps/cpsaat39.htm (Accessed 25 Feb, 2016).

Answer 1

ANS.

OBS.	X	X^2
1	566	320356
2	648	419904
3	767	588289
4	683	466489
5	604	364816
6	727	528529
7	751	564001
8	614	376996
9	664	440896
10	516	266256
11	675	455625
12	467	218089
13	680	462400
14	655	429025
15	638	407044
16	627	393129
SUM =	10282	6701844