Reconsider the previous exercise about memorization with and without music.
a. The standard deviation of the null distribution shown is 0.974. Use this to find an approximate 95% confidence interval for the mean difference in the number of words memorized (no music ˆ’ music) for the population of interest.
b. Based on your confidence interval from part (a), is there strong evidence that people can memorize words better when music is not playing compared to when it is? Explain.

Data from previous question

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:

Transcribed Image Text:

No music With music Difference Mean 2.30 12.80 10.50 Standard deviation 3.15 3.38 3.76