Which of the following best describes the null hypothesis of a $\chi 2^{ }$ goodness of fit test?

• A. The observed frequencies are significantly different from the expected frequencies.
• B. The sample mean $\mu$ is equal to the population mean $\mu$.
• C. The data are normally distributed.
• D. The observed frequencies are consistent with the expected frequencies under the specified distribution.

Answer: (D)

Verified step by step guidance

1. Understand that the chi-square goodness of fit test is used to determine if observed categorical data fits a specified distribution.
2. Recall that the null hypothesis (\(H_0\)) in this test states that the observed frequencies match the expected frequencies according to the hypothesized distribution.
3. Recognize that the alternative hypothesis (\(H_a\)) states that the observed frequencies differ significantly from the expected frequencies.
4. Note that the null hypothesis does not involve means or assumptions about normality; it specifically concerns the consistency between observed and expected counts.
5. Therefore, the null hypothesis can be formally stated as: \(H_0\): The observed frequencies are consistent with the expected frequencies under the specified distribution.