10.151 [EX10-151] At a large university, a mathematics placement exam is administered to all students.

This exam has a history of producing scores with a mean of 77. Samples of 36 male students and 30 females students are randomly selected from this year’s student body and the following scores 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), mean, and standard deviation.

b. Test the hypotheses, “Mean score for all males is 77” and “Mean score for all females is 77,”

using   0.05.

c. Do the preceding results show that the mean scores for males and females are the same?

Justify your answer. Be careful!

d. Test the hypothesis, “There is no difference between the mean scores for male and female students,” using   0.05.

e. Do the results found in part d show that the mean scores for male and females are the same? Explain.

f. Explain why the results found in part b cannot be used to conclude, “The two means are the same.”