Final answer:
The t-distribution is not typically used for testing a proportion since proportions usually involve categorical data and are better suited for a normal distribution given a large enough sample size. The t-distribution is reserved for estimating a population mean with unknown standard deviation and a smaller sample size, assuming a normally distributed underlying population.
Step-by-step explanation:
Typically, the t-distribution is not used in testing a proportion; it is primarily used when estimating a population mean, especially with a small sample size or when the population standard deviation is unknown. For testing a proportion, the test statistic is usually based on the normal distribution, assuming a large enough sample size for the Central Limit Theorem to apply. This is because we are often dealing with categorical data in a proportion problem, which when large enough, even if originating from a binomial distribution, can be approximated by a normal distribution.
Hypothesis testing for a proportion using a normal distribution would typically be the correct procedure. However, if the sample size is not large enough for the normal approximation to be valid, a different distribution or test might be required, although not typically the t-distribution. The setup for hypothesis testing of proportions involves comparing the sample proportion to a population parameter or another sample proportion to determine if there is a significant difference reflecting true population differences.
Furthermore, the Student's t-distribution is generally reserved for situations related to means rather than proportions. This includes cases involving matched or paired samples where a t-test is appropriate as well. However, this would still require the assumption that the underlying population is normally distributed especially when the data are not from a simple random sample.