Numerous studies have demonstrated that listening to music while studying can improve memory (Hallam, Price, & Katsarou, 2002). To demonstrate this phenomenon, a researcher obtains a sample of college students and gives them a standardized memory test while they are listening to background music. Under normal circumstances (without music), the scores on the test form a normal-shaped distribution with a mean of u = 25 and a standard deviation of o = 6. The sample produces a mean score of M=28.
a. If the sample consists of n=4 students, is this result sufficient to conclude that the music had a significant effect on memory scores? Use a two-tailed test with alpha = .05 Be sure to show all formulas, include all steps and plug in the numbers (show all work). Explain the decision to reject or fail (significant or not significant effect).
b. If the sample consists of n=36 students, is this result sufficient to conclude that the music had a significant effect? Again, use a two-tailed test with alpha = .05 Be sure to show all formulas, include all steps and plug in the numbers (show all work). Explain the decision to reject or fail (significant or not significant effect).
c. If there is a difference in outcomes (overall significance), what can you conclude about the results of part a and b above?