19.1. Car insurance savings. A large car insurance company with thousands of customers advertises that customers switching to their insurance save, on average, 50 on their yearly premiums. A market researcher at a competing insurance discounter is interested in showing that this value is an overestimate so she can provide evidence to government regulators that the company is falsely advertising their prices. She randomly samples 89 customers who recently switched to this insurance and finds an average savings of 48.48. with a standard deviation of 10.32. (a) Are conditions for inference used in the lectures satised? [b] What is your null hypothesis? (c) What is your alternative hypothesis? (d) Assuming conditions for inference from the lectures are satisfied, calculate the pvalue for a one-sided hypothesis test. (e) What is your conclusion if the test was conducted at a significance level of a = 0.05? (f) Would you agree with the market researcher that the amount of savings adver- tised is definitely an overestimate based on this sample? [Make sure you can explain your reasoning] (g) Calculate a 90% confidence interval for the average amount of savings of all customers who switch their insurance. [in] Do your results from the hypothesis test and the condence interval agree? [Make sure you can explain your reasoning] [1.5] [1] [2] [0.51 [0.51 [2] [0.51