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 - with music) is O (ud O) Alternative: The average of the difference in number of words memorized (no music - with music) is greater than 0 (ud> 0) The students found the following results in terms of number of words memorized Mean Standard deviation No musicWith music Difference 10.50 3.15 12.80 3.38 2.30 3.76 The standard deviation of the null distribution is 0.974. Use this to find an approximate 95% confidence interval for the mean difference in the number of words memorized (no music music) for the population of interest. Round your answers to 3 decimal places, e.g. 5.836. Confidence interval

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? Yes, because the confidence interval includes 0/ No, because the confidence interval includes 0/ Yes, because the confidence interval does not include 0/ No, because the confidence interval does not include 0

Answer 1

Paired T-Test and CI

N Mean StDev SE Mean
Difference 20 10.500 3.150 0.704

95% CI for mean difference: (9.026, 11.974)
T-Test of mean difference = 0 (vs not = 0): T-Value = 14.91 P-Value = 0.000

Ans: 95% CI for mean difference (=no music-music): (9.026, 11.974)

Yes, because the confidence interval does not include 0.

Note: More reasonable option is: Yes, because the confidence interval contains only positive values.