Question

A prospective MBA student would like to examine the factors that impact starting salary upon graduation and decides to develop a model that uses program per year tuition as a predictor of starting salary. Data were collected for 37 full-time MBA programs offered at private universities. The data are stored in the accompanying table. The least squares regression equation for these data is Y = -13,799.046 +2.420X, and the standard error of the estimate is Syx = 16,513.295. Assume that the straight-line model is appropriate and there are no serious violations the assumptions of the least squares regression model. Complete parts (a) and (b) below Click the icon to view the data on program per year tuition and mean starting salary a. At the 0.10 level of significance, is there evidence of a linear relationship between the starting salary upon graduation and program per year tuition? Determine the hypotheses for the test

Answer 1

a.

Hypothesis:

$\\ H_0:\beta_1 = 0 \\ H_1:\beta_1 \neq 0$

Test statistic,

$\\ t=\frac{\hat{\beta_1}}{SE\hat{\beta_1}} \sim t_{n-2} \\ \\ \\ t = \frac{2420}{16513.295} \\\\\\ t= 0.15$

Degrees of freedom = 37 - 2 = 35

P-value = 0.882

It is obtained by using excel with function, =TDIST(0.15,35,2)

Since p-value is greater than 0.10,

Fail to reject H0. There is not sufficient evidence to conclude that there is linear relationship between starting salary upon graduation and program per year tution.

b.

90% confidence interval:

$\\ C.I. = \hat{\beta_1} \pm t_{\alpha /2,df} * SE(\hat{\beta_1}) \\ \\ C.I. = 2420 \pm 1.690 * 16513.295 \\ \\ C.I. = (-25487.469 , 30327.469)$