Which of the following is an important application of the $\chi 2^2$ distribution?

• A. Estimating the mean of a $N$ population with unknown variance
• B. Testing whether observed categorical data fit an expected distribution using the goodness of fit test
• C. Comparing the means of two independent samples
• D. Calculating the correlation coefficient between two variables

Answer: (B)

Verified step by step guidance

1. Understand that the chi-square distribution is primarily used in hypothesis testing involving categorical data rather than continuous data like means or correlations.
2. Recall that one key application of the chi-square distribution is the goodness of fit test, which assesses whether observed categorical data match an expected distribution.
3. Recognize that estimating the mean of a normal population with unknown variance typically involves the t-distribution, not the chi-square distribution.
4. Note that comparing the means of two independent samples is usually done using a t-test, which also does not involve the chi-square distribution.
5. Understand that calculating the correlation coefficient between two variables involves correlation or regression analysis, which does not use the chi-square distribution.