College IDAccept rate (%)Grad rate (%)

1596

2795

3893

4994

51196

61492

71592

81693

91691

101892

111890

121996

132090

142389

152488

162678

172787

182785

192883

202980

Q2. Pearson's Correlation (15 points)

It is generally believed that there is a relationship between a college's acceptance rate and its graduation rate. I wanted to know how strong this relationship is within the top universities in the country so I collected the graduation rate and acceptance rate data of a randomly selected sample of universities from all the top U.S. universities (with an acceptance rate at or below 30%). The data set is in Tab Q2 of the Excel data file.

b. Calculate the mean and standard deviation for the two variables separately.

c. Calculate the Z scores for all the scores of the two variables, separately. Tips: It may help to prevent error and to increase clarity if the process and/or the answers (z scores) are listed in a table format.

d. Calculate Pearson's correlation coefficient r.

e. Explain the direction and strength of the relationship based on the r.

f. What is the proportion of variance shared between the two variables? (That is, how much of the variance in one variable can be predicted by the variance in the other variable?)

g. If the researcher wants to perform a two-tailed hypothesis test using this data set so that she can generalize the relationship between the two variables from the sample to the population, what would be the null and alternative hypothesis? Write the hypotheses in words and in symbol notation.

h. Using SPSS to analyze the same dataset yields a p value of .001. Based on = .05, what would be the conclusion of the hypothesis test (use wording of "reject the null hypothesis" or "fail to reject the null hypothesis"? How do you know?