Final answer:
This mathematics question focuses on statistical concepts such as mean, standard deviation, and what distribution to use for hypothesis testing. It's a high school level math question. The correct distribution to use in this case would be the t-distribution due to the sample size being less than 30 and the assumption of normality.
Step-by-step explanation:
The subject of this question is clearly within the field of Mathematics, particularly involving the use of statistics. It discusses concepts such as mean or expected value, standard deviation, sample size, and confidence intervals. These are fundamental topics covered in high school mathematics and introductory college statistics courses. The question is likely part of a problem set designed to teach students about descriptive statistics and inferential statistics, including how to calculate these values and make predictions about a larger population based on sample data.
To answer the specific question about what distribution should be used for a hypothesis test when we have a population mean of 13, a sample mean of 12.8, a sample standard deviation of two, and a sample size of 20, assuming the underlying population is normal, one should use a t-distribution. Since the sample size is less than 30, and we're assuming a normal population distribution, the t-distribution is appropriate for making inferences about the population mean.