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?

Question

Fletcher Garner

Mathematics

19 June, 02:02

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?

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Aydan Carney · Answer 1

Step-by-step 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.