A Human Resource selected two samples of employees, one containing only men and the other containing only women, to look for evidence of possible discrimination in pay. From the sample of 36 men, they determined the salaries had a mean of $75,000 and a standard deviation of $16,250. In the sample of 58 women, the mean salary was just $68,000 with a standard deviation of $18,642. Although the men in the sample were paid $7,000 more on average than the women, is this enough evidence to conclude that there is difference in the mean salaries of the larger populations of male and female employees from which these samples were selected? Claim: The population of male employees are paid more on average than the population of female employees. 1. Express the hypothesis set for evaluating the claim. Make sure to: a. Clearly indicate which hypothesis is the null (H0) and which is the alternative (H1). b. Use the correct Greek letter symbol to describe the population parameters. Use the subscripts M to identify the parameters of the male population and F to identify the parameters of the female population. c. Use the appropriate comparison symbols (e.g. >, =, , etc.) 2. You will be performing a 2-sample t-test to compare the means assuming equal population variances, at a 1% significance level ( =1%). Determine the degrees of freedom and the t-critical value. Report both. 3. State the decision rule you will use to evaluate your test results. Your decision rule must compare the sample test statistic to the critical value. 4. Calculate the sample test statistic. Show ALL the work in your calculations and circle or highlight your final answer. 5. Use the t-table to look up the p-value (it will be a range, not a specific number) that reflects your result. 6. Analyse the result of the test by doing the following things: a. Tell me whether or not you are rejecting H0 b. Tell me if the conclusion from 6a would stay the same if you used = 5% or 10% instead of 1%. Explain how you know. c. Tell me what the HR professional has learned about the salaries of the male and female populations