Conduct a following hypothesis test:

a two tail T test for a two sample difference in means at the 95% confidence level

with Null hypothesis that the men's salaries and women's salaries are equal

and with the Alternate Hypothesis that the men's salaries and women's salaries are unequal

Women 241,649 292,508 177,973 302,631 240,740 330,995 394,437 293,739 328,970 346,404

Men 358,474 341,123 298,762 299,473 391,191 266,833 343,028 216,698 288,741 381,053

a Calculate the mean and standard deviation of the salaries for each group

b. Using the correct degrees of freedom (df= # of men + # of women - # of groups), the correct number of tails, and the correct confidence level, determine the critical value of t.

c Explain under which scenario using a pooled variance be inadvisable, then, calculate the pooled variance for the groups

d Calculate the test statistic, T test

e The states system's statistician tells you that p-value for the test is 0.1089. Summarize the result of the study. Compare mean salaries in each group. Compare the test statistic to the critical value. Compare p-value to alpha. Do you find a statistically significant difference between men salaries and women salaries for nurses in the state hospital system? Is there a meaningful/practical difference? Explain your decisions and justify your claims