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 (music – no music) in the number of words memorized is 4.1 words with a standard deviation of 3.8 words. Assuming that the conditions for inference are met, what is the P-value for testing the hypotheses H0 :μdiff = 0; Ha :μdiff > 0?Find the t-table here.
This is a paired t-test with 14 volunteers, so the degrees of freedom are 14 − 1 = 13. The test statistic is t = 4.1 ÷ (3.8/√14) ≈ 4.04. For 13 degrees of freedom, the one-sided P-value for t ≈ 4.04 is about 0.0007, matching choice A, 0.0007.
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