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Assume you are working at the Consumer Protection Agency. Recently, you have been getting complaints about the highway gas mileage of a new minivan. The car company agrees to allow you to select randomly 41 of its new minivans to test their highway mileage. The company claims that its minivans get 28 miles per gallon on the highway. Your test results show a sample mean of 26.7 and a sample standard deviation of 4.2. Part 1 (Confidence Interval): Calculate a 95% confidence interval around your sample mean. Is the claimed mean inside your confidence interval? What does your result mean, in terms of the company's claim? Part 2 (Two-tail test): List the null and alternative hypotheses for the appropriate test. Use alpha = 0.05. Find the critical value(s) and calculate the observed value of the test statistic. Is the observed test statistic in the critical (rejection) region? Will the p-value be higher or lower than your alpha? What does this result mean, in terms of the company's claim? Part 3 (One-tail test): List the null and alternative hypotheses for the test. Use alpha = 0.05. Find the critical value and calculate the observed value of the test statistic. Is the observed test statistic in the critical region? Will the p-value be higher or lower than your alpha? What does this result mean, in terms of the company's claim?

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