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 40 of its new minivans to test their highway mileage. The company claims that its minivans get 28 miles per gallon on the highway. Your results show a mean of 26.7 and a standard deviation of 4.2. You are not certain if you should create a confidence interval or run a hypothesis test. You decide to do both at the same time. You run a one-tail test, two-tail test, and a confidence interval. You decide to accept an alpha risk of 0.05. Part 1 (Confidence Interval): Calculate the confidence interval. Draw the bell-shaped curve, the upper and lower boundaries of the confidence interval and the sample mean. Draw a vertical line representing the claimed mean. Is the claimed mean inside your confidence interval? Part 2 (Two-tail test): List the null and alternative hypotheses for the two-tail test. Calculate the critical values and observed value of the test statistic. Draw a picture of a bell-shaped curve with the critical test statistics. Add a vertical line for the observed test statistic. Is the observed test statistic in the critical region? Will the p-value be higher or lower than your alpha? Part 3 (One-tail test): List the null and alternative hypotheses for the one-tail test. Calculate the critical value and observed value of the test statistic. Draw a picture of a bell-shaped curve with the critical test statistics. Add a vertical line for the observed test statistic. Is the observed test statistic in the critical region? Will the p-value be higher or lower than your alpha? Part 4 (Conclusion): In your write-up, address at least the following: What conclusions did you reach? Specifically, what did you learn from each method? Were there important differences between methods? Which method would you prefer? Which carries a higher risk of a type I error? Based on this experience, why do you think it's important to decide on the method before conducting the test? Note: The 1- to 2-page requirement does not include the graphs you prepare for this Assignment. Embed the graphs you create in the Word document with your written responses to the questions. Drawings may be hand-drawn and either scanned or photographed, or they may be drawn using Minitab or other statistical drawing packages