A researcher is testing the effect of listening to music while studying on memory. She obtains a sample of 36 college students and gives them a standardized memory test while they are listening to background music. Their mean is found to be 28. Under normal circumstances (without music) the scores on the test form a normal shaped distribution with a population mean of 25 and a standard deviation of 6. Is the result sufficient to conclude that music has a significant effect on memory? Test at α = .05. 

a. Using symbols, state the null and alternative hypotheses.

b. Assuming  = .05, what critical value should the researcher use to test her hypothesis that music affects memory?  

c. Calculate the z-score statistic for this sample. 

d. What decision should the researcher make about the null hypothesis? 

e. What conclusion should the researcher reach about the effect of music on memory?