Math 215 - Statistical Concepts Name: ______________________ HOW DO YOU MAKE INFORMED DECISIONS? Problem 1: A market research survey asked the question \"Do you enjoy shopping for clothing for yourself?\" to 542 male adults and 238 of them said they did. When 543 female adults were asked the same question, 276 of them indicated that they enjoyed shopping for clothing for themselves. (Source: USA Today) a. Is there a significant difference between the proportion of males and females who enjoy shopping for clothing for themselves at the 0.05 level of significance? Perform a hypothesis test to make an informed decision. Show your work or calculator commands. b. Find a 95% and confidence interval for the difference between the proportions of males and females who enjoy shopping for clothing for themselves. Show your work or calculator commands. Does this interval support your decision in part a? Problem 2: In a study of women's science majors the following data on grade point averages (GPA) and selfesteem 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 X Leavers 3.16 Stayers 3.28 Leavers 3.05 Stayers 2.96 s1 n1 0.52 103 0.46 225 0.75 103 0.75 225 Source: Paula Raymann and Belle Brett, The Journal of Higher Education 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 = 0.05. Show your work or calculator commands. b) Find a 95% confidence interval for the difference between the grade point averages of leavers and stayers. Show your work or calculator commands. c) Explain whether your findings in part a) and b) conflict or support each other. 280415 Math 215 - Statistical Concepts Name: ______________________ d) Test the claim that those who stayed in their science profession had a lower self-esteem than those who left. Use = 0.05.What is your decision? Show your work or calculator commands. e) Find a 95% confidence interval for the difference between the average self-esteem scores of leavers and stayers. Show your work or calculator commands. f) Explain whether your findings in part d) and e) conflict or support each other. 280415