Do district teachers' CCSS approval levels align with the national distribution? Which test is used?

Do district teachers' CCSS approval levels align with the national distribution? Which test is used?

• A. Chi-square test of independence
• B. Chi-square goodness-of-fit with 4 degrees of freedom
• C. ANOVA
• D. Paired t-test

Answer: (B)

You're testing whether the distribution of district teachers across CCSS approval levels matches the national distribution. That calls for a chi-square goodness-of-fit test, which compares observed counts in each category to the counts expected if the national distribution applied. This approach is appropriate because you have one categorical variable (approval level) and you’re checking against a specified distribution, not examining relationships between two variables or comparing averages. It isn’t about independence (which looks at two variables) and not about comparing means (which would involve ANOVA or a t-test). The degrees of freedom come from the number of categories minus one, reflecting how many independent deviations you can observe across the categories. If the observed counts diverge noticeably from the expected counts, you’d conclude there’s misalignment between district and national distributions. Ensure assumptions like independent observations and sufficiently large expected counts are met for a valid result.

You're testing whether the distribution of district teachers across CCSS approval levels matches the national distribution. That calls for a chi-square goodness-of-fit test, which compares observed counts in each category to the counts expected if the national distribution applied. This approach is appropriate because you have one categorical variable (approval level) and you’re checking against a specified distribution, not examining relationships between two variables or comparing averages. It isn’t about independence (which looks at two variables) and not about comparing means (which would involve ANOVA or a t-test). The degrees of freedom come from the number of categories minus one, reflecting how many independent deviations you can observe across the categories. If the observed counts diverge noticeably from the expected counts, you’d conclude there’s misalignment between district and national distributions. Ensure assumptions like independent observations and sufficiently large expected counts are met for a valid result.