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In a study of women's science majors the following data on grade point averages (GPA) and self-esteem scores of two groups were obtained. The two groups are those who left their profession within a few months after graduation (leavers) and those who remained in their profession after they graduated (stayers). GPA Self-Esteem Leavers Stayers Leavers Stayers X 3.16 3.28 3.05 2.96 S1 0.52 0.46 0.75 0.75 n1 103 225 103 225 Source: Paula Raymann and Belle Brett, The Journal of Higher Education CLEARLY HANDWRITE STEPS AND ANSWERS a) Do you think that there is enough evidence to claim that those who stayed in their science profession had a higher grade point average than those who left? Perform a hypothesis test and use a = 0.05. Show your work. b) Find a 95% confidence interval for the difference between the grade point averages of leavers and stayers. Show your work. c) Explain whether your findings in part a) and b) conflict or support each other. d) Test the claim that those who stayed in their science profession had a lower self-esteem than those who left. Use a = 0.05.What is your decision? Show your work. e) Find a 95% confidence interval for the difference between the average self-esteem scores of leavers and stayers. Show your work. f) Explain whether your findings in part d) and e) conflict or support each other