Question

The CEO of a large company claims that 85% of customers are repeat customers. They define a repeat customer as someone who makes more than one purchase per month. A random sample of 200 customers shows that 162 are repeat customers. Do these data provide convincing evidence at the 5% significance level that less than 85% of customers of this company are repeat customers?

Are the conditions for inference met?
Random: We have a random sample of .
10%: 200 customers < 10% of .
Large Counts: There are expected successes and expected failures, which are both at least .

Answer 1

A company CEO says that 85% of their customers are repeat customers. A sample of 200 customers was taken, and it was found that 162 of them were repeat customers. We want to know if this sample supports the CEO's claim, or if it suggests that less than 85% of the company's customers are repeat customers. We performed a statistical test and found that the sample provides evidence at a significance level of 5% that less than 85% of customers are repeat customers. The conditions for this test are met because the sample was taken randomly, and the sample size is small enough compared to the overall population size.