Assume you are working at the Consumer Protection Agency. Recently, you have been getting complaints about the highway gas mileage of new Dodge Caravans. Chrysler Corporation agrees to allow you to select randomly 40 of its new Dodge Caravans to test their highway mileage. Chrysler claims that the Caravans vans 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:
Part 1:
• Draw a normal curve, labeling the critical values, critical regions, test statistic, and population mean. List the significance level and the null and alternative hypotheses.
• Draw a confidence interval directly below the normal distribution, labeling the sample mean, error, and boundary values.
• Explain which parts from each approach are the same and which parts are different.
Part 2:
• Draw a picture of a normal curve and confidence interval where the sample and hypothesized means are equal.
• Draw a picture of a normal curve and confidence interval where the lower boundary of the confidence interval is equal to the hypothesized mean.
• Draw a picture of a normal curve and confidence interval where the sample mean falls in the left critical region of the normal curve.
The graphs should be attached to the end of the paper.