Question

a. Explain why a goodness-of-fit test and a test of independence are generally right-tailed tests.

b. If you did a left-tailed test, what would you be testing?

Short answer

a). If observed values and expected values are not close together, then the test statistic can get very large.

b). To do left-tailed test, test for s single variance can be applied.

Step-by-step solution

Given Information (Part a)

A goodness-of-fit test and a test of independence are generally right-tailed tests.

Explanation (Part a)

The chi-square curve is always right-tailed because of degrees of freedom. It can be noticed that for degrees of freedom two the curve can be exponential. But with higher degrees of freedom, the curve will be drawn as right-skewed. Researcher always claims that observed frequencies are close to the expected frequencies. If observed frequencies are close to expected frequencies, then the square of deviations will be small and the graph will be right-tailed. After that, the square of deviations is divided by the expected frequency to weight frequencies. It can be noticed that the difference of $5$ is very significant if 7 was the expected frequency, but a difference of $5$ is not significant if the expected frequency was $700$. Therefore, if observed values and expected values are not close together, then the test statistic can get very large.

Given Information (Part b)

If you did a left-tailed test, what would you be testing?

Explanation (Part b)

To do left-tailed test, test for $s$ single variance can be applied.