In a chi-square goodness of fit test, what does the null hypothesis ($H\_0$) specify about the population proportions or frequencies?

• A. The null hypothesis ($H\_0$) states that all observed frequencies are equal to each other.
• B. The null hypothesis ($H\_0$) specifies the expected proportions or frequencies for each category in the population.
• C. The null hypothesis ($H\_0$) assumes that the sample size is too small to detect any differences.
• D. The null hypothesis ($H\_0$) specifies that the observed frequencies are always greater than the expected frequencies.

Answer: (B)

Verified step by step guidance

1. Understand that the chi-square goodness of fit test is used to determine if the observed frequencies in different categories match the expected frequencies based on a specific hypothesis about the population.
2. Recall that the null hypothesis (denoted as \(H_0\)) in this test specifies the expected distribution of frequencies or proportions across the categories, which means it defines what the population proportions or frequencies should be if there is no difference.
3. Recognize that the null hypothesis does NOT state that all observed frequencies are equal to each other; rather, it states that the observed frequencies come from the population with the specified expected proportions.
4. Note that the null hypothesis does not make assumptions about sample size being too small or about observed frequencies always being greater than expected frequencies; these are incorrect interpretations.
5. Summarize that the null hypothesis in a chi-square goodness of fit test specifies the expected proportions or frequencies for each category in the population, serving as the baseline for comparison with observed data.