Question

1. Suppose we would like to determine if the typical amount spent per customer for dinner at a new restaurant in town is more than $20.00.  A sample of 49 customers over a three-week period was randomly selected and the average amount spent was $22.60.  Assume that the standard deviation is known to be $2.50.

•Using a 95% confidence level of significance, would we conclude the typical amount spent per customer is more than $20.00?

•Discuss your interpretation of your findings.

2. Suppose an editor of a publishing company claims that the mean time to write a textbook is at most 15 months.  A sample of 16 textbook authors is randomly selected and it is found that the mean time taken by them to write a textbook was 12.5.  Assume also that the standard deviation is known to be 3.6 months.

•Assuming the time to write a textbook is normally distributed and using a 95% confidence level of significance, would you conclude the editor’s claim is true?  

•Discuss your interpretation of your findings.

**Please show all work**

Answer 1

Concept:4

We do hypothesis testing to validate the claims. Whatever the claim is made, we take that as an alternate hypothesis and the complementary as a null hypothesis. We run the p-value test to find evidence about the claim. If the p-value is less than the confidence level of significance, we reject the null and conclude that the claim made is true.

Please find the solution. In one problem I have used p-value and in other directly compared Z value