Chapter 9, Problem 72PS

The owner of a speciality coffee shop wants to study coffee purchasing habits of customers at her shop. She selected a random sample of 60 customers during a certain week, with the following results:

$•$ The amount Spent was $\bar{X}=\$7.25,S=\text{\$1}\text{.75}\text{.}$

$•$ Thirty-one customers say they “definitely willâ€� recommend the specialty coffee shop to family and friends.

a. At the 0.05 level of significance, is there evidence that the population mean amount spent was different from $\$6.50?$

b. Determine the p-value in (a).

c. At the 0.05 level of significance, is there evidence that more than $50\%$ of all the customers say they “definitely will� recommend the speciality coffee shop to family and friends?

d. What is your answer to (a) if the sample mean equals $\text{\$}6.25?$

e. What is your answer to (c) if 398 customers say that “definitely will� recommend the speciality coffee shop to family and friends?