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Hypothesis test: correlation coefficient

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Coastal State University is conducting a study regarding the possible relationship between the cumulative grade point average and the annual income of its recent graduates. A random sample of 151 Coastal State graduates from the last five years was selected, and it was found that the sample correlation coefficient between cumulative grade point average and annual income was 0.21.

Test for a significant linear relationship between grade point average and annual income for the recent graduates of Coastal State by doing a hypothesis test regarding the population correlation coefficient rho. (assume that the two variables have a bivariate normal distribution.) Use the 0.05 level of significance, and perform a two tailed test. Then fill in the table below.

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This solution shows details of a hypothesis test regarding a correlation coefficient and the slope of a least squares regression line.

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