Question

Recall that the number of degrees of freedom for the t-distribution used in a one-mean t-test depends on the sample size. Is that true for the chi-square distribution used in a chi-square.

Part (a): Goodness-of-fit test?

Part (b): Independence test?

Part (c): Homogeneity test?

Explain your answers.

Short answer

Part (a): No. The degrees of freedom for the chi-square goodness-of-fit test depends only upon the number of possible values for the variable under consideration.

Part (b): No. The degrees of freedom for the chi-square independence test depends only upon the number of possible values for the two variables under consideration.

Part (c): No. The degrees of freedom for the chi-square homogeneity test depends only upon the number of possible values for the variable under consideration.

Step-by-step solution

Part (a) Step 1. Given information.

It is given that the number of degrees of freedom for the t-distribution used in a one-mean t-test depends on the sample size.

Part (a) Step 2. Goodness-of-fit test is used.

The number of degrees of freedom for the t-distribution which is used in one-mean t-test depends on the sample size. While the chi-square distribution used in a chi-square goodness-of-fit test is not true as the degrees of freedom for the chi-square goodness-of-fit test under consideration depends on the number of possible values for the variable and not on the sample size.

Part (b) Step 1. Independence test is used.

The number of degrees of freedom for the t-distribution which is used in a one-mean t-test depends on the sample size. The chi-square distribution used in a chi-square independence test is not true as the degrees of freedom for the chi-square independence test under consideration depends on the number of possible values for the two variables and not on the sample size.

Part (c) Step 1. Homogeneity test is used.

The number of degrees of freedom for the t-distribution which is used in a one-mean t-test depends on the sample size. The chi-square distribution used in a chi-square homogeneity test is not true as the degrees of freedom for the chi-square homogeneity test under consideration depends on the number of possible values for the variable and not on the sample size.