You are working at a firm that conducts independent testing for heavy industry. Recently, an automobile manufacturer has been in the news for complaints about the highway gas mileage of their latest model minivan. You receive a contract from a consumer action group to test and report on the company's claim that its minivans get 28 miles per gallon on the highway. The car company agrees to allow you to select randomly 35 low-mileage fleet minivans to test their highway mileage. Your test results gave you the following data:

29.7	24.5	27.1	29.8	29.2	27.0	27.8	24.1	29.3
25.9	26.2	24.5	32.8	26.8	27.8	24.0	23.6	29.2
26.5	27.7	27.1	23.7	24.1	27.2	25.9	26.7	27.8
27.3	27.6	22.8	25.3	26.6	26.4	27.1	26.1

1. Calculate a 95% confidence interval around your sample mean.
2. Is the company's claimed mean inside your confidence interval?
3. What does that result indicate about the company's claim?

Complete the following and include your results and responses in your report (use alpha = 0.05):

1. List the null and alternative hypotheses for the two-tail test for the mean. Calculate the observed value of the test statistic and the associated p-value. (Include calculations)
   • Is the observed test statistic in the critical region?Is the p-value higher or lower than your alpha? (Include calculations)
2. List the null and alternative hypotheses for the one-tail test of the mean. Calculate the observed value of the test statistic and the associated p-value. (Include calculations)
   • Is the observed test statistic in the critical region?Will the p-value be higher or lower than your alpha? (Include calculations)

Use the confidence interval information and the results of the hypothesis testing to provide support for your conclusions and recommendations to the company. Specifically:

1. What conclusions can be reached? What can be learned about learned about the situation by using each method? Does one method offer more conclusive proof than another?
2. Based on the results, is the company's claim that their minivans get 28 miles per gallon supported?
3. Summarize the details of the test methods and the results from each statistical method used. Explain the findings so that executives from both the agency and the company can understand the conclusion.
4. What recommendations for actions that the company might take to use the findings to better serve their customers in the future?