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# Hypothesis tests for Correlation Coefficient

A nationwide standardized test taken by high-school juniors and seniors may or may not measure academic potential, but we can nonetheless examine the relationship between scores on such tests and performance in college.

We have chosen a random sample of 105 students just finishing their first year of college, and for each student we've recorded her score on one such standardized test and her grade point average for her first year in college. For our data, the least-squares regression equation relating the two variables score on this standardized test (denoted by x and ranging from 400 to 1600 ) and first-year college grade point average (denoted by y and ranging from 0 to 4 ) is y .8887 + .0022x . The standard error of the slope of this least-squares regression line is approximately.

Based on these sample results, test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population slope b1. (Assume that the variable follows a normal distribution for each value of and that the other regression assumptions are satisfied.) Use the .10 level of significance, and perform a two-tailed test. Then fill in the table below.

(If necessary, consult a list of formulas.)

ho=
h1=
value of test statistic
and critical values at the .10 significance(round three decimals) ? & ?

#### Solution Preview

Ho: b1 = 0

H1: b1 <> 0

t- score

t = Slope of the regression line / ...

#### Solution Summary

The solution studies hypothesis tests for correlation coefficient.

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