Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

Exercise 30

Expand Your Knowledge: Student's t Value for Sample r and for Sample b It is not obvious from the formulas, but the values of the sample test statistic t for the correlation coefficient and for the slope of the least-squares line are equal for the same data set. This fact is based on the relation.

where s y and s x are the sample standard deviations of the x and y values, respectively.
(a) Many computer software packages give the t value and corresponding P -value for b. If is significant, is significant
(b) When doing statistical tests "by hand," it is easier to computer the sample test statistic t for the sample correlation coefficient r than it is to compute the sample test statistic t for the slope b of the sample least-squares line. Compare the results of parts (b) and (f) for Problems 7-12 of this problem set. Is the sample test statistic t for r the same as the corresponding test statistic for b If you conclude that is positive, can you conclude that is positive at the same level of significance If you conclude that is not significant, is also not significant at the same level of significance