The sampling distribution of the population correlation coefficient is ____ when the population coefficient is equal to 0.
A)positively skewed
B)negatively skewed
C)symmetrical and approximately normal
D)bimodal

Question

Quizplus · Accepted Answer

When the population correlation coefficient is equal to 0, the sampling distribution of the correlation coefficient is symmetrical and approximately normal. This means that the distribution forms a bell curve around 0, with the majority of the sample correlation coefficients clustering around 0. This is because when the population correlation is 0, there is no linear relationship between the two variables, and any observed correlation coefficients are due to chance alone. The central limit theorem also supports the normality assumption when sample sizes are large enough. Therefore, option C is the correct answer.

The Sampling Distribution of the Population Correlation Coefficient Is ____