Question

use the hypothesis test for linear correlation flow chart interactive to answer the following question.
a null hypothesis of $h_0: \
ho = 0$ is equivalent to which one of the following?

choose the correct answer below.

a. there is no linear correlation.

b. there is a negative linear correlation.

c. there is a linear correlation.

d. there is a positive linear correlation.

Explanation:

In the context of linear correlation, the population correlation coefficient is denoted by \(
ho \). A null hypothesis \( H_0:
ho = 0 \) means we are testing the claim that there is no linear relationship between the two variables. Option A states "There is no linear correlation," which matches the meaning of \(
ho = 0 \). Option B refers to negative correlation (where \(
ho < 0 \)), Option C is a general linear correlation (which would be tested with \( H_1:
ho
eq 0 \) or similar for positive/negative), and Option D is positive correlation (where \(
ho > 0 \)). So the correct interpretation of \( H_0:
ho = 0 \) is no linear correlation.

Answer:

A. There is no linear correlation.