Vendors of hearing aids test them by having patients listen to lists of words and repeat what they hear. The word lists are supposed to be equally difficult to hear accurately. But the challenge of hearing aids is perception when there is background noise. A researcher investigated four different word lists used in hearing assessment (Loven, 1981). She wanted to know whether the lists were equally difficult to understand in the presence of a noisy background. To find out, she tested 24 subjects with normal hearing and measured the number of words perceived correctly in the presence of background noise. Here are the boxplots of the four lists.

a) What are the null and alternative hypotheses?
b) What do you conclude?
c) Would it be appropriate to run a multiple comparisons test (for example, a Bonferroni test) to see which lists differ from each other in terms of mean percent correct? Explain.

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45 40 25 15 10F 6 List1 List 2 List 3 List 4 List Sum of Mean Source DF Squares Sque F-ratio P-value List 3 920.4583 306.819 4.9192 0.0033 Error 92 5738.1667 62.371 Total 95 6658.6250 2 2