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 professional and related occupation sector in 2015 was $1343. Vera collected median weekly earnings data for women in 2015 from a random subset of 18 positions in the professional and related occupation sector. The following is the sample data. $1811, $728, $1234, $966, $953, $1031, $990, $633, $796, $1325, $1448, $1125, $1144, $1082, $1145, $1256, $1415, $1170 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=1343H0:μ=1343 against the alternative hypothesis, H1:µ<1343H1:μ<1343 , where µμ 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⎯⎯⎯x¯ , of Vera's sample. Report your answer with two decimals of precision.

Answer 1

Answer:

There is sufficient evidence to conclude that women make less money than men doing the same job.

Step-by-step explanation:

The hypothesis for the test can be explained as follows:

H₀: Women does not make less money than men doing the same job, i.e. $\mu\geq \ 1343$.

Hₐ: Women make less money than men doing the same job, i.e. $\mu$.

From the provided data compute the sample mean and standard deviation:

$\bar x=\frac{1}{n}\sum X=\frac{1}{18}[1811+728+...+1170]=1125.11\\\\s=\sqrt{\frac{1}{n-1}\sum (X-\bar x)^{2}}=\sqrt{\frac{1}{18-1}\times 1322541.86}=278.92$

Compute the test statistic as follows:

$t=\frac{\bar x-\mu}[\s/\sqrt{n}}=\frac{1125.11-1343}{278.92/\sqrt{18}}=-3.143$

The test statistic value is -3.143.

Compute the p-value as follows:

$p-value=P(t_{n-1}$

*Use a t-table.

The p-value of the test is 0.003.

The p-value of the test is very small for all the commonly used significance level. The null hypothesis will be rejected.

Conclusion:

There is sufficient evidence to conclude that women make less money than men doing the same job.