A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store.Fifteen credit card accounts were randomly sampled and analysed with the following results: $\bar { X }$ = $50.50 and S = 20.
-Assuming the distribution of the amount spent on their first visit is approximately normal,what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for $\mu$?
A) A t distribution with 15 degrees of freedom.
B) A standard normal distribution.
C) Approximately normal with a mean of $50.50.
D) A t distribution with 14 degrees of freedom.

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean for a small sample size (n < 30) from a population with an approximately normal distribution and an unknown population standard deviation is best described by a t distribution with degrees of freedom equal to n - 1, which in this case is 15 - 1 = 14.

A Major Department Store Chain Is Interested in Estimating the Average