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 recorded:

a. Describe each set of data with a histogram (use the same class intervals on both histograms), the mean, and the 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 the 95% confidence interval for the difference between the mean scores for male and female students.
e. Do the results found in part d show that the mean scores for male and female students could be the same? Explain.
f. Explain why the results in part b cannot be used to draw conclusions about the difference between the two means. 

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Male 72 68 75 82 8 60 75 85 80 70 71 84 68 85 82 80 54 8 86 79 99 90 68 82 60 63 72 77 51 61 71 8 74 79 76 Female 81 76 94 89 83 78 85 91 83 83 84 80 84 88 77 74 63 9 80 82 89 69 74 97 73 79 55 76 78 81