A music professor is interested in the effects of listening to music while memorizing a list of words. She asks 14 volunteers to memorize two different lists of words: one list while listening to music in the background and the other list with no music in the background. The order of the treatments is determined by a coin toss. The mean difference open paren music minus no music close paren in the number of words memorized is 4 point 1 words with a standard deviation of 3 point 8 words. Assuming that 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 1 minus 0 and denominator displaystyle the fraction with numerator 3 point 8 and denominator square root of 14
B
t is equal to the fraction with numerator 0 minus 4 point 1 and denominator displaystyle the fraction with numerator 3 point 8 and denominator square root of 14
C
t is equal to the fraction with numerator 0 minus 4 point 1 and denominator displaystyle square root of 3 point 8 over 14 end root
D
t = the fraction with numerator 4 point 1 minus 0 and denominator displaystyle square root of 3 point 8 over 14 end root
Explanation
For paired data, the test statistic is t = (mean difference − hypothesized difference)/(standard deviation of the differences/√n). Substituting the values gives t = (4.1 − 0)/(3.8/√14), which is about 4.04. This matches choice A.
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