Use the following to answer questions 1-7
1992–1993 salary data for a sample of 15 universities was obtained. We are curious about the relationship between mean salaries for assistant professors (junior faculty) and full professors (senior faculty) at a given university. In particular, do universities pay (relatively) high salaries to both assistant and full professors, or are full professors treated much better than assistant professors? In other words, do senior faculty receive high salaries compared to other universities while junior faculty receive relatively low salaries? Suppose we fit the following simple linear regression model
Full Prof. Salaryi = b0 + b1(Asst. Prof. Salary)i + ei
where the deviations ei were assumed to be independent and normally distributed, with mean 0 and standard deviation s. The variables Full Prof. Salary and Asst. Prof. Salary are the mean salaries for full and assistant professors at a given university. This model was fit to the data using the method of least squares. The following results were obtained from statistical software. Note that salaries were in thousands of dollars. Mean assistant professor salaries were treated as the explanatory variable and mean full professor salaries as the response variable.
R2 = 0.596
s = 5.503
Variable
Parameter Est.
Std. Err. of Parameter Est.
Constant
15.0658
14.36
Asst. Prof. Salary
1.40827
0.3217
1. The intercept of the least-squares regression line is (approximately)
15.07.
14.36.
1.41.
0.32.
2. A 90% confidence interval for the slope b1 in the simple linear regression model is (approximately)
1.41 ± 0.57.
1.41 ± 0.32.
–1.41 ± 0.57.
–1.41 ± 0.32.
3. Suppose the researchers test the hypotheses
H0: b1 = 0, Ha: b1 ¹ 0.
The value of the t statistic for this test is
0.32.
1.05.
1.41.
4.38.
4. The correlation between mean assistant and full professor salaries is
0.055.
0.355.
0.596.
0.772.
5. The degrees of freedom for residual MS, the mean sum of squares for error, is
13.
14.
15.
not able to be determined from the information given.
6. The value of residual MS, the mean sum of squares for error, is
0.3217.
5.503.
30.28.
not able to be determined from the information given.
7. Suppose we wish to test the hypotheses
H0: r = 0, Ha: r ¹ 0
where r is the population correlation between mean assistant and full professor salaries. The value of the t statistic for testing this hypothesis is
0.596
0.772
4.38
6.89