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.

 

 

Q2b. 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 0.5 if an answer is incorrect but the calculation process was correct]

 

 

Q2c. 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]

 

 

Q2d. Calculate Pearson’s correlation coefficient r.
[2 points total: 1 if the process is correct but the answer is wrong]

 

Q2e. Explain the direction and strength of the relationship based on the r.
[1 point total: 0.5 for strength, 0.5 for direction]

 

 

Q2f. 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?) (Do not round during the calculation, the final result as the percentage should be to the hundredth [2^nd decimal])
[1 point total: -0.5 if the process is correct but the answer is wrong]

 

 

 

Q2g. 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, 0.5 for written, 0.5 for symbol notation]

 

	Written	Symbolic Symbol bank for copy & pasting: £ = ³ < ¹ > m r
Null
Alternative

 

Q2h. Using SPSS to analyze the same dataset yields a p value of .026. 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: 0.5 for conclusion, 0.5 for rationale]

 

 

 

 

Information Provided:

 

College ID	Accept rate (%)	Grad rate (%)
1	5	96
2	5	97
3	8	90
4	3	95
5	12	94
6	10	91
7	18	84
8	15	93
9	12	84
10	16	92
11	20	87
12	18	96
13	20	91
14	20	82
15	24	86
16	26	76
17	25	86
18	28	82
19	25	78
20	30	76