Step 1 of 3: Each year a nationally recognized publication conducts its Survey of America’s Best Graduate and Professional Schools. An academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. A least-squares regression line of SALARY versus GMAT is y = -92040 + 228x, and the correlation, r, is 0.81. If the sample size used to create the regression line is n=20, is r statistically significant at a 0.05 level?

Step-by-step explanation:

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Given the variables

Y: Starting salary of a graduate at a top business school

X: GMAT score of the business school

The sample used had a size n=20

The estimated regression equation was ^Y= -92040 + 228Xi

The correlation coefficients were r= 0.81

You need to know if r is statistically significant at a 0.05 level:

Assuming the hypotheses are:

H₀: There is a linear correlation between the variables of interest

H₁: There is no linear correlation between the variables of interest

α: 0.05

This test is two-tailed.

The p-value for a r=0.81 and n=20 is 0.000015

Using the p-value approach, the decision rule is:

If p-value ≤ α, reject the null hypothesis

If p-value > α, do not reject the null hypothesis

In this case, the p-value is less than α, the decision is to reject the null hypothesis.

At a 5% level, you can conclude that the coefficient of correlation is statistically significant.

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