Which of the following is true? I. In a t-test for a single population mean, inc

Question

Which of the following is true? I. In a t-test for a single population mean, increasing the sample size (while everything else the same) changes the number of degrees of freedom used in the test. II. In a chi-square test for independence, increasing the sample size (while everything else the same) changes the number of degrees of freedom used in the test. III. In a t-test for the slope of the population regression line, increasing the number of observations (while leaving everything else the same) changes the number of degrees of freedom used in the test. (A) I only (B) I and II only (C) I and III only (D) II and III only (E) I, II and III

Explanation / Answer

I. In a t-test for a single population mean, the number of degrees of freedom is given by n-1. As sample size(n) increases, number of degrees of freedom(n-1) also increases. i.e. I is true.

II. In a chi-square test for independence, the number of degrees of freedom is depend on number of categories and not depend on sample size(n) . i.e. II is not true.

III. In a t-test for the slope of the population regression line, the number of degrees of freedom is given by n-2. As sample size(n) increases, number of degrees of freedom(n-2) also increases. i.e. III is true.

• (C) is correct. i.e. I and III is true.

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