Q1

THE SCENARIO: Imagine you are a market researcher who works for SaveSmart, a discount insurance company. The company's management has become aware of some dissatisfaction among customers who have switched to SaveSmart from other insurance carriers. They want you, their market researcher, to determine if the majority of customers who have switched to SaveSmart really are dissatisfied with the switch, and if the dissatisfaction could stem from their advertised claim that customers on average save $432 on their yearly premiums. You start with the $432 amount that is advertised as the average yearly savings. You want to check to see if this is perhaps an overestimate of the amount actually saved. You randomly sample 82 customers who switched to SaveSmart from another insurance carrier, and find an average savings of $415 with a standard deviation of $102. 1) Complete the 6 steps for a hypothesis test at the 5% level of significance to determine if the $432 average savings is an overestimate. 2) Calculate a 90% confidence interval for the average amount of savings of all customers who switch their insurance to SaveSmart. Interpret the interval in this context and comment on whether or not the confidence interval agrees with the conclusion of the hypothesis test