Does listening to music affect how many words you can memorize? Student researchers tried to answer this question by having 20 subjects listen to music while trying to memorize words and also had the same 20 subjects try to memorize words when not listening to music. They randomly determined which condition was done first for each of their subjects. Here are their hypotheses:

Null: The average of the difference in number of words memorized (no music ˆ’ with music) is 0 (μ_d = 0).
Alternative: The average of the difference in number of words memorized (no music ˆ’ with music) is greater than 0 (μ_d > 0).
The students found the following results in terms of number of words memorized:

a. What is the explanatory variable in this study? Is it categorical or quantitative?

b. What is the response variable in this study? Is it categorical or quantitative?
c. What is the observed statistic in this study?

d. Assuming a true null hypothesis, we simulated this study and found 1,500 mean differences that are shown in the null distribution below. Based on where the observed statistic lies in this distribution, does the p-value appear to be fairly small?

e. Th e standard deviation of the null distribution is 0.974. Use this to find the standardized statistic for this test.
f. Based on your standardized statistic from part (e), is there strong evidence that people can memorize words better when music is not playing compared to when it is? Explain.

Transcribed Image Text:

No music With music Difference Mean 2.30 12.80 10.50 Standard deviation 3.15 3.38 3.76 Average difference Mean = -0.0090 SD = 0.974 -4 -2 -1 2 3 -0.01 Average difference