Redo the preceding exercise, this time using the mathematics scores.

Preceding Exercise

Use the reading comprehension data in Exercise 6.18 to test the null hypothesis that the population mean of X is 0.
a. What is the two-sided P value?
b. Does the average value of X seem substantially different from 0?

Exercise 6.18

An outside consultant for a small suburban private school with a reputation for academic excellence analyzed the test scores in Table 6.4 for 13 students (of the 20 students initially admitted) who stayed at the school from first grade through eighth grade. The scores are percentiles relative to students at suburban public schools. For example, on the first-grade reading comprehension test, Student A’s score was higher than the scores of 79 percent of the students at suburban public schools. Calculate the difference X between the eighth-grade and first-grade reading comprehension scores for these 13 students. Assuming these are a random sample from a hypothetical population of students attending this school over the years, calculate a 95 percent confidence interval for a population mean of X.

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Table 6.4: Exercise 6.18 Reading Comprehension Student First Grade Eighth Grade First Grade Mathematics Eighth Grade ABCDEFGH 79 33 81 57 91 38 93 51 98 92 97 98 99 75 99 74 94 4 96 34 98 75 96 91 99 68 98 95 97 33 93 78 99 68 98 90 J 99 99 96 67 KLM 99 9 97 53 97 86 97 67 91 86 96 83