Which of the following is not a characteristic of the $t$ test?

• A. It is appropriate for small sample sizes.
• B. It is only used for categorical data.
• C. It assumes the data are normally distributed.
• D. It is used when the population standard deviation is unknown.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the purpose of the t-test. The t-test is a statistical test used to compare the means of two groups, especially when the sample size is small and the population standard deviation is unknown.
2. Step 2: Review the assumptions of the t-test. These include: (a) the data should be approximately normally distributed, and (b) the samples are independent.
3. Step 3: Recognize that the t-test is used for continuous numerical data, not categorical data. Categorical data typically require different tests, such as the chi-square test.
4. Step 4: Analyze each statement given: (a) 'It is appropriate for small sample sizes' is true; (b) 'It assumes the data are normally distributed' is true; (c) 'It is used when the population standard deviation is unknown' is true; (d) 'It is only used for categorical data' is false because the t-test is not designed for categorical data.
5. Step 5: Conclude that the statement 'It is only used for categorical data' is not a characteristic of the t-test, making it the correct answer to the question.