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 cap p -value 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 ? Use the t -table.
Because the same 14 volunteers experienced both conditions, use a paired t-test with 14 − 1 = 13 degrees of freedom. The test statistic is t = 4.1 ÷ (3.8/√14) ≈ 4.04. For 13 degrees of freedom, the t-table places this one-sided tail probability between 0.001 and 0.002, so the closest listed p-value is 0.0014, choice D.
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