Question

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

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. (4 points total: 1 point for each mean and 1 point for each SD, deduct .5 if an answer is in correct but the calculation process was correct)

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.

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

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

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

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?) (1 point total: -.5 if the process is correct but the answer is wrong)

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. (2 points total: 1 for each hypothesis, .5 for written, .5 for symbol notation)

h. Using SPSS to analyze the same dataset yields a p value of .001. Based on α = .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? (1 point total: .5 for conclusion, .5 for rationale)

Answer 1

Dear student, we can answer only four subparts at a time, please help to upload other parts separately.

b)

For accept rate, the mean comes out to be 18% whereas the standard deviation comes out to be 7.5%

For grad rate, the mean comes out to be 90% whereas the standard deviation comes out to be 5.19%

c)

The z-scores comes out to be -

We will be calculating it in the excel.

Accept rate	Grad rate	z scores(accept rate)	z scores(grad rate)
5	96	-1.74	1.16
7	95	-1.47	0.96
8	93	-1.34	0.58
9	94	-1.20	0.77
11	96	-0.93	1.16
14	92	-0.53	0.39
15	92	-0.40	0.39
16	93	-0.27	0.58
16	91	-0.27	0.19
18	92	0.00	0.39
18	90	0.00	0.00
19	96	0.13	1.16
20	90	0.27	0.00
23	89	0.67	-0.19
24	88	0.80	-0.39
26	78	1.07	-2.31
27	87	1.20	-0.58
27	85	1.20	-0.96
28	83	1.34	-1.35
29	80	1.47	-1.93

d)

It comes out to be -0.84.

e)

The relation between the two variables is negative, which means if one increases, the other decreases and vice-versa. It's a strong negative relationship.