A 1-Sample t-test is used when you want to compare the Median of one distribution to a target value.

The statement is false. The 1-Sample t-test is a parametric hypothesis test used to compare the mean of a single sample to a specified target or hypothesized population mean. It is not designed to test the median. The test statistic is calculated using the sample mean, sample standard deviation, and sample size. For hypotheses concerning a population median, non-parametric tests such as the 1-Sample Sign Test or the 1-Sample Wilcoxon Signed-Rank Test are the appropriate statistical tools to use.

A. True: This is incorrect. The fundamental purpose of the 1-Sample t-test is to make inferences about a population mean, not its median.

1. Montgomery, D. C. (2013). Introduction to Statistical Quality Control (7th ed.). John Wiley & Sons. In Chapter 4, Section 4-3, "Inference on the Mean of a Normal Distribution, Variance Unknown," the text explicitly defines the procedure for hypothesis testing on the mean (μ) using the t-statistic.

2. The Pennsylvania State University. (n.d.). STAT 500: Applied Statistics. Eberly College of Science. In Lesson 5.2, "One-Sample Mean t-test," the course material states, "A one sample t-test is used to test whether a population mean is equal to some value." It makes no mention of the median.

3. University of Michigan. (n.d.). One-sample t-test. School of Public Health, Biostatistics. Course materials for Biostat 521 state, "The one-sample t-test is used to test a hypothesis about a single population mean μ when the population standard deviation σ is unknown."