Pennsylvania Refining Company is studying the relationship b

Pennsylvania Refining Company is studying the relationship between the pump price of
gasoline and the number of gallons sold. For a sample of 20 stations last Tuesday, the
correlation was .78. At the .01 significance level, is the correlation in the population
greater than zero?

Solution

As

t = r sqrt [(n - 2) / (1 - r^2)]

Then as r = 0.78, n = 20,

t = 5.288

As this is a right tailed test (greater than 0), then the critical t value at alpha = 0.01, df = n-2 = 18, is

tcrit = 2.55237963

As t > tcrit, then we REJECT THE NULL HYPOTHESIS.

We have a significant evidence that the correlation in the population is greater than 0. [CONCLUSION]