Question

use the hypothesis test for linear correlation flow chart interactive to answer the following question. twenty pairs of data result in a linear correlation coefficient of r = 0. if using a t test for testing the claim that there is a linear correlation, what is the value of the t test statistic? choose the correct answer below. a. 18 b. 1 c. 0 d. 20

Explanation:

Step1: Recall t-test formula for correlation

The formula for the t - test statistic for testing the claim of a linear correlation is \( t=\frac{r\sqrt{n - 2}}{\sqrt{1-r^{2}}} \), where \( r \) is the correlation coefficient and \( n \) is the number of pairs of data.

Step2: Substitute values

We are given that \( r = 0 \) and \( n=20 \). Substitute these values into the formula:
\( t=\frac{0\times\sqrt{20 - 2}}{\sqrt{1-0^{2}}}=\frac{0\times\sqrt{18}}{\sqrt{1}}=\frac{0}{1} = 0 \)

Answer:

C. 0