Question

A sample of 7 department store sizes (in thousands of square feet) and revenues (in millions of dollars) are found to have a linear coefficient of 0.445. Find the critical values for the linear correlation coefficient, assuming a 0.05 significance level. Is there sufficient evidence to conclude that there is a linear correlation between size and revenue of department stores?

Answer 1

Critical values = ±0.754; there is not sufficient evidence to conclude that there is a linear correlation between size and revenue of department stores.

Answer 2

Explanation:

The test statistic is:

t = r √((n − 2) / (1 − r²))

Given r = 0.445 and n = 7:

t = 0.445 √((7 − 2) / (1 − 0.445²))

t = 1.111

Using a t table, the critical value for 0.05 significant level and 6 degrees of freedom is 1.943.

Since t < 1.943, there is no linear correlation.