A car insurance company advertises that customers switching to their insurance save, on average, $432 on their yearly premiums. A market researcher at a competing insurance discounter is interested in showing that this value is an overestimate so he can provide evidence to government regulators that the company is falsely advertising their prices. He randomly samples 82 customers who recently switched to this insurance and finds an average savings of $395, with a standard deviation of $102.
(a) Are conditions for inference satisfied?
(b) Perform a hypothesis test and state your conclusion.
(c) Do you agree with the market researcher that the amount of savings advertised is an overestimate? Explain your reasoning.
(d) Calculate a 90% confidence interval for the average amount of savings of all customers who switch their insurance.
(e) Do your results from the hypothesis test and the confidence interval agree? Explain.