For which of the following scenarios is a chi-square $\chi 2^{}$ goodness-of-fit test most appropriate?

• A. Estimating the population mean $\mu$ from a sample mean $𝑛$ and standard deviation $s$.
• B. Assessing the linear relationship between two continuous variables.
• C. Testing whether the observed frequencies of colors in a bag of candies match the expected distribution of colors.
• D. Comparing the means $𝑛$ of two independent samples to determine if they are significantly different.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the purpose of a chi-square goodness-of-fit test. This test is used to determine if the observed frequencies of categories in a sample match the expected frequencies based on a specific theoretical distribution.
2. Step 2: Review each scenario to see if it involves comparing observed categorical frequencies to expected frequencies. The first scenario involves estimating a population mean, which is a parameter estimation problem, not frequency comparison.
3. Step 3: The second scenario involves assessing the linear relationship between two continuous variables, which is typically done using correlation or regression analysis, not a chi-square test.
4. Step 4: The third scenario involves testing whether the observed frequencies of colors in a bag of candies match the expected distribution of colors. This directly involves categorical data and frequency comparison, making it suitable for a chi-square goodness-of-fit test.
5. Step 5: The fourth scenario involves comparing means of two independent samples, which is usually done with a t-test, not a chi-square test. Therefore, the chi-square goodness-of-fit test is most appropriate for the third scenario.