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 20 randomly selected universities from all the top U.S. universities (with an acceptance rate at or below 30%). 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. 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? 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 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?
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 20 randomly selected universities from all the top U.S. universities (with an acceptance rate at or below 30%).
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.
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?
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 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?
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