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2) The development office and the registrar have provided you with anonymous matches of starting salaries and GPAs for 110 graduating economics majors. Your sample contains a variety of jobs, from church pastor to stockbroker. (a) The average starting salary for the 110 students was $38,644 with a standard deviation of $7,541. i) Construct a 95% confidence interval for the starting salary of all economics majors at your university/college. Calculate the lower-limit and upper-limit. (10%) ii) Interpret this 95% Cl. (5%) (b) You wonder if it pays (no pun intended) to get good grades by calculating the average salary for economics majors who graduated with a cumulative GPA of B+ or better, and those who had a B or worse. The data is as shown in the accompanying table. Cumulative GPA B+ or better B or worse Average Earnings Y $39,915 $37,083 Standard deviation Sy $8,330 $6,174 n 60 50 Conduct a t-test for the hypothesis that the two starting salaries are the same in the population. (a) Set up the null and alternative hypotheses. (5%) (b) Calculate the t-value for this data. (5%) (c) What critical value should you choose at the 5% level of significance. Show the rejection and non-rejection areas on a graph. (5%) (d) Calculate the p-value for this data and interpret it. (5%) (e) Using the results from the sample, can you reject the null hypothesis? Explain. (5%)