"10.50 At a large university, a mathematics placement exam is administered to all students. Samples of 36 male and 30 female students are randomly selected from this year's student body and the following scores are recorded:
Male 72 68 75 82 81 60 75 85 80 70
71 84 68 85 82 80 54 81 86 79
99 90 68 82 60 63 67 72 77 51
61 71 81 74 79 76
Female 81 76 94 89 83 78 85 91 83 83
84 80 84 88 77 74 63 69 80 82
89 69 74 97 73 79 55 76 78 81

a. Describe each set of data with a histogram (use the same class intervals on both histograms) the mean, standard deviation.
b. Construct 95% confidence interval for the mean score for all male students. Do the same for all Female Students.
c. Do the results found in part b show that the mean scores for males and females could be the same? Justify your answer. Be Careful!
d. Construct a 95% confidence interval for the difference between the mean scores for the male and female students.
e. Do the results found in part d show the mean scores for the male and females students could be the same? Explain
f. Explain why the results in part b cannot be used to draw a conclusion about the difference between the two means.
g. Analyze the problem and type a short summary (1-2 paragraphs) of the results.