Question

Which of the following is not one of the conditions that must be satisfied in order to perform inference about the slope of a least-squares regression line?

a. For each value of $x$, the population of y-values is Normally distributed.

b. The standard deviation σ of the population of $y$-values corresponding to a given value of $x$is always the same, regardless of the specific value of $x$.

c. The sample size—that is, the number of paired observations ($x,y$)—exceeds $30$.

d. There exists a straight line such that, for each value of $x$, the mean $\mu y$of the corresponding population of $y$-values lies on that straight line.

e. The data come from a random sample or a randomized experiment.

Short answer

Option (c) is the correct option.

Step-by-step solution

Step 1. Given information

a. For each value of $x$, the population of $y$-values is Normally distributed.

b. The standard deviation $\sigma$of the population of $y$-values corresponding to a given value of $x$is always the same, regardless of the specific value of $x$.

c. The sample size—that is, the number of paired observations ($x,y$)—exceeds $30$.

d. There exists a straight line such that, for each value of $x$, the mean $\mu y$of the corresponding population of $y$-values lies on that straight line.

e. The data come from a random sample or a randomized experiment.

Step 2. Explanation for correct option

Now, in the question we have to find out that which of these is not one of the conditions that must be satisfied in order to perform inference about the slope of a least-square regression line. Thus, we know that there are five conditions in order to perform inference about the slope of a least-squares regression line, that are: Random, Normal, Independent, Linear, Equal variance.

Thus, by looking at the options to get that:

Option (a) must be satisfied because it is the Normal requirement.

Option (b) must be satisfied because it is the Equal variance requirement.

Option (c) must not be satisfied because we require no limitations on the sample size.

Option (d) must be satisfied because it is the Linear requirement.

Option (e) must be satisfied because it is the Random requirement.

Thus, we have option (c) is not one of the condition that must be satisfied in order to perform inference about the slope of a least-square regression line.