Which test is appropriate to assess if observed counts across several categories fit a specified distribution?

Which test is appropriate to assess if observed counts across several categories fit a specified distribution?

• A. 1-Proportion Z-Test
• B. 2-Sample T-Test
• C. Chi-Square Goodness-of-Fit Test
• D. Fisher's Exact Test

Answer: (C)

Assessing whether observed counts across several categories fit a specified distribution is what the chi-square goodness-of-fit test does. You calculate how many observations you’d expect in each category if the data truly followed the specified distribution (E_i = N × p_i, where N is the total count and p_i are the specified probabilities). Then you compare the observed counts to these expected counts using the sum of (O_i − E_i)² / E_i across all categories. A large sum indicates the data diverge from the specified distribution, while a small sum suggests agreement. Degrees of freedom are the number of categories minus one (adjusted if any probabilities are estimated from the data). The other options don’t fit this purpose. A 1-proportion z-test looks at a single category’s proportion, not multiple categories. A 2-sample t-test compares means between two groups, which is about numerical data rather than counts in categories. Fisher’s Exact Test is used for small-sample contingency tables to test association between variables, typically in 2×2 tables, not goodness-of-fit across many categories.

Assessing whether observed counts across several categories fit a specified distribution is what the chi-square goodness-of-fit test does. You calculate how many observations you’d expect in each category if the data truly followed the specified distribution (E_i = N × p_i, where N is the total count and p_i are the specified probabilities). Then you compare the observed counts to these expected counts using the sum of (O_i − E_i)² / E_i across all categories. A large sum indicates the data diverge from the specified distribution, while a small sum suggests agreement. Degrees of freedom are the number of categories minus one (adjusted if any probabilities are estimated from the data).

The other options don’t fit this purpose. A 1-proportion z-test looks at a single category’s proportion, not multiple categories. A 2-sample t-test compares means between two groups, which is about numerical data rather than counts in categories. Fisher’s Exact Test is used for small-sample contingency tables to test association between variables, typically in 2×2 tables, not goodness-of-fit across many categories.