In: Statistics and Probability
. USA Today reported that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice. Suppose that Chevrolet did a study of a random sample of 1006 Chevrolet owners and found that 490 stated that they would buy another Chevrolet. Test the claim by Chevrolet that the population proportion of consumers loyal to its product is different from 47%. Use = 0.05. (a) State the hypotheses for this test. (b) State the p-value for this test. (c) State your conclusion for the test in the context of the problem statement. (d) Give a 95% confidence interval for the proportion of customers loyal to Chevrolet. (e) Is your confidence interval consistent with your conclusion from the hypothesis test? Explain why or why not.