A realtor wanted to investigate whether there is a linear relationship between the number of square feet in a house and the selling price. The realtor collected data on 49 randomly selected homes for sale in Virginia Beach and used the data to test the claim that there is a linear relationship. The following hypotheses were used to test the claim:

\[H_0: \beta_1 = 0\]
\[H_a: \beta_1 \neq 0\]

The test yielded a test statistic of 2.07 and a corresponding p-value of 0.04496. Which of the following is the correct interpretation of the p-value?

A. If there is not a linear relationship between the number of square feet and the selling price, the probability of observing a test statistic of 2.07 is 0.04496.

B. If there is not a linear relationship between the number of square feet and the selling price, the probability of observing a test statistic of 2.07 or greater is 0.04496.

C. If there is a linear relationship between the number of square feet and the selling price, the probability of observing a test statistic at least as extreme as 2.07 is 0.04496.

The p-value interpretation is that if there is a linear relationship between square footage and selling price, the probability of observing a test statistic as extreme as 2.07 is 0.04496. Option (c) is correct.

Explanation:

The correct interpretation of the p-value in this scenario is option c.

This means that if there is a linear relationship between the number of square feet and the selling price, the probability of observing a test statistic at least as extreme as 2.07 is 0.04496.

This interpretation is based on the p-value obtained from the hypothesis test conducted by the realtor to determine the existence of a linear relationship between square footage and selling price.