Using basic demographic information (age, household income, marital status, etc.), you collect a random sample size 185 customers who accepted a special balance transfer offer from a major credit card company six months ago. The company wants to determine if there is evidence that it would profit by offering the deal to the population of customers with those same demographic characteristics. The sample mean balance transfer amount is 1,421 with a sample standard deviation of 484.

Based on the information above, if the company were to perform a hypothesis test at = 0.05, what is the largest value it could specify in the null hypothesis and still fail to reject the null hypothesis?

Hint: Think about the relationship between hypothesis tests and intervals. Specifically, think about how a test done at alpha equal 0.05 would relate to a 95% confidence interval?

2.

The manufacturer of Twitchy Energy Drink is doing a quality inspection to make sure that the caffeine content of the drink is meeting specifications of 79.6 mg per can. Suppose a quality inspector takes a sample of size 13 from the production line and finds that the average caffeine content in the sample is 78.4 mg, with a standard deviation of 0.32 mg.

Calculate the test statistic for testing the hypothesis that the true mean caffeine content is less than 79.6 mg per can. Report your answer to two decimal places.