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T test for correlation coefficient

A correlation coefficient for Bee Taylor's Department Store in Mayberry, NC, between sales ability and amount of sales is Sales ability is measured on an interval scale and amount of sales is measured on a ratio scale. Note that the correlation was conducted on 42 sales employees. Test this coefficient by using a t test and Table B.2. This test was mentioned in "Tech Talk" on page 263. However, the author never showed the formula, which can be found in many statistics books.

Below is the "famous" formula.

t = r . This formula tells you to multiply the coefficient by the square root of the df divided by the difference of 1 and the coefficient squared. Note that n = sample size; df (degrees of freedom) = the sample size decreased by 2.

H0: and H1:

(a) Critical value t at 5% risk =

(b) Obtained test statistic (Show procedure.): t =

(c) Decision on H0:

(d) What conclusion do you reach about sales ability and amount of sales? Are these variables at Bee's correlated?

Review the problem above.

(a) What percent of sales volume is explained by sales ability?

(b) Express the relationship between sales ability and sales volume that is suggested by the correlation coefficient. Write in terms of strength and direction of the relationship.


Solution Preview


a) Critical value t at 5% risk = ± 2.02
b) Obtained test statistic (Show procedure.): t = 6.376
c) on H0: Reject the H0. ...

Solution Summary

The solution provides step by step method for the calculation of t test statistic for correlation coefficients . Formula for the calculation and Interpretations of the results are also included.