1 of 2 Q + CD A v v G QZ 19.1. Car insurance savings. A large car insurance company with thousands of customers advertises that customers switching to their insura ave, on average, 150 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 148.48, with a standard deviation of 210.32. (a) Are conditions for inference used in the lectures satisfied? [1.5) (b) What is your null hypothesis? [1] (c) What is your alternative hypothesis? [1] (d) Assuming conditions for inference from the lectures are satisfied, calculate the p-value for a one-sided hypothesis test. [21 (e) What is your conclusion if the test was conducted at a significance level of a = 0.05? [0.5] (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.] [0.5) (g) Calculate a 90% confidence interval for the average amount of savings of all customers who switch their insurance. (h) Do your results from the hypothesis test and the confidence interval agree? [Make sure you can explain your reasoning.] [0.5] (i) Write the function confidence_interval(n,a, mu, sigma) to give you the 100xa% confidence interval with mean of u (mu), standard deviation of o (sigma), and sample size n. Return the confidence intervals as a vector i.e c(lower confidence interval, upper confidence interval) [2] QZ 19.2. Identify distributions. Four plots are presented below. The plot at the top is a distribution for a population. The mean is 60 and the standard deviation is 18. Also shown below is a distribution of 1. a single random sample of 500 values from this population, 2. a distribution of 500 sample means from random samples of each size 81, 3. a distribution of 500 sample means from random samples of each size 18 Determine which plot (A, B, or C) is which and make sure you can justify your reasoning- 65 60 Plot A Plat C