It is generally believed that there is a relationship between acollege’s acceptance rate and its graduation rate. I wanted to knowhow strong this relationship is within the top universities in thecountry so I collected the graduation rate and acceptance rate dataof a randomly selected sample of universities from all the top U.S.universities (with an acceptance rate at or below 30%).

College ID	Accept rate (%)	Grad rate (%)
1	5	96
2	7	95
3	8	93
4	9	94
5	11	96
6	14	92
7	15	92
8	16	93
9	16	91
10	18	92
11	18	90
12	19	96
13	20	90
14	23	89
15	24	88
16	26	78
17	27	87
18	27	85
19	28	83
20	29	80

b. Calculate the mean and standard deviation for the twovariables separately. (4 points total: 1 point for each mean and 1point for each SD, deduct .5 if an answer is in correct but thecalculation process was correct)

Acceptance rate:

Mean = 18

SD = 7.3

Grad Rate

Mean = 90

SD = 5.06

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

(2 points total: 1 for Z scores for each variable)

d. Calculate Pearson’s correlation coefficient r. (2points total: 1 if the process is correct but the answer iswrong)

e. Explain the direction and strength of the relationship basedon the r. (1 point total: .5 for strength, .5 fordirection)

f. What is the proportion of variance shared between the twovariables? (That is, how much of the variance in one variable canbe predicted by the variance in the other variable?) (1 pointtotal: -.5 if the process is correct but the answer is wrong)

g. If the researcher wants to perform a two-tailed hypothesistest using this data set so that she can generalize therelationship between the two variables from the sample to thepopulation, what would be the null and alternative hypothesis?Write the hypotheses in words and in symbol notation. (2 pointstotal: 1 for each hypothesis, .5 for written, .5 for symbolnotation)

h. Using SPSS to analyze the same dataset yields a pvalue of .001. Based on α = .05, what would be the conclusion ofthe hypothesis test (use wording of “reject the null hypothesis” or“fail to reject the null hypothesis”? How do you know? (1 pointtotal: .5 for conclusion, .5 for rationale)