The principal of a large high school wants to improve student test scores, so he asks one of his science teachers to try a new method of teaching. Thirty-one students take a pretest on the first day of science class. After 6 weeks using the new instruction, the same students take a posttest. The mean difference open paren posttest minus pretest close paren in scores is 4 point 8 points with a standard deviation of 9 point 7 points. Assuming the conditions for inference are met, what is the test statistic for testing the hypotheses ratio of cap h sub 0 to mu sub diff is equal to 0 ; ratio of cap h sub A to mu sub diff is greater than 0 ?
Answer
A
t is equal to the fraction with numerator 4 point 8 minus 0 and denominator displaystyle the fraction with numerator 31 and denominator square root of 9 point 7
B
t is equal to square root of the fraction with numerator 0 minus 4 point 8 and denominator 9 point 7 end root
C
t is equal to the fraction with numerator 4 point 8 minus 0 and denominator displaystyle the fraction with numerator 9 point 7 and denominator square root of 31
D
t is equal to the fraction with numerator 0 minus 4 point 8 and denominator displaystyle the fraction with numerator 31 and denominator square root of 9 point 7
Explanation
For a one-sample t test on the paired differences, use t = (sample mean difference − hypothesized mean difference) / (standard deviation of differences / √n). Substituting the values gives t = (4.8 − 0) / (9.7 / √31), which is choice C. The denominator is the standard error of the mean difference.
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