Question

(a) What assumptions must you make in order to use these statistics for inference? Select all that apply. t. The sample of 43 weekdays is representative of all days. B. The distribution of sample week

Answer 1

In hypothesis testing using a Student's t-distribution, it's assumed that the sample is random, the population is normally distributed for small samples, and the Student's t-distribution is used when the population standard deviation is unknown and the sample size is small.

Step-by-step explanation:

Assumptions for Hypothesis Testing Using a Student's t-Distribution

When performing hypothesis testing of a single population mean using a Student's t-distribution, several assumptions must be made:

• The sample is a random sample from the population.
• The population from which the sample is drawn is normally distributed if the sample size is small. For larger samples, the distribution need not be perfectly normal due to the Central Limit Theorem.
• When the population standard deviation is unknown, and the sample size is small, the Student's t-distribution is used.

These assumptions are essential for the valid application of t-tests to estimate population parameters and make inferences. Failing to meet these criteria can result in inaccurate conclusions.