To assess whether a new sample of grades matches a historical grade distribution (A through F with specified percentages), which test is appropriate?

To assess whether a new sample of grades matches a historical grade distribution (A through F with specified percentages), which test is appropriate?

• A. Chi-square goodness-of-fit
• B. Chi-square test of independence
• C. t-test for proportions
• D. ANOVA

Answer: (A)

This tests whether observed frequencies across grade categories match a predefined distribution. When data are categorical and you have a specific theoretical distribution for how often each category should occur, the chi-square goodness-of-fit test is the appropriate tool. It checks if the actual counts in each grade (A through F) align with the historical percentages by comparing observed counts to expected counts (total sample size times each grade’s historical proportion). The test statistic sums (observed − expected)² divided by the expected for all categories, and you judge significance using a chi-square distribution with k−1 degrees of freedom, where k is the number of grade categories. Why this fits here: you’re not exploring relationship between variables or comparing means; you’re evaluating whether a single categorical distribution matches a specified benchmark. The other tests aren’t suited for this purpose: a chi-square test of independence looks at relationships between two categorical variables, a t-test for proportions compares a sample proportion to a value (or compares two proportions) but not an entire distribution across multiple categories, and ANOVA compares means across groups rather than frequencies in categories.

This tests whether observed frequencies across grade categories match a predefined distribution. When data are categorical and you have a specific theoretical distribution for how often each category should occur, the chi-square goodness-of-fit test is the appropriate tool. It checks if the actual counts in each grade (A through F) align with the historical percentages by comparing observed counts to expected counts (total sample size times each grade’s historical proportion). The test statistic sums (observed − expected)² divided by the expected for all categories, and you judge significance using a chi-square distribution with k−1 degrees of freedom, where k is the number of grade categories.

Why this fits here: you’re not exploring relationship between variables or comparing means; you’re evaluating whether a single categorical distribution matches a specified benchmark. The other tests aren’t suited for this purpose: a chi-square test of independence looks at relationships between two categorical variables, a t-test for proportions compares a sample proportion to a value (or compares two proportions) but not an entire distribution across multiple categories, and ANOVA compares means across groups rather than frequencies in categories.