Question

Using basic demographic information (age, household income, marital status, etc.), you collect a random sample size 190 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 1,935 with a sample standard deviation of 424. Based on the information above, if the company were to perform a hypothesis test at α = 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 equals 0.05 would relate to a 95% confidence interval?

Answer 1

As long as value corresponding to null hypothesis is within confidence interval, it cannot be rejected. So the largest value of null hypothesis that the company could specify and fail to reject the null hypothesis is the upper confidence limit of 95% confidence interval.

95% Confidence interval calculation:

The largest value = Upper confidence limit = 1995.677