Question

For this Assignment, 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 write a 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

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

• 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. (75–150 words, or 1–2 paragraphs)
  • Is the observed test statistic in the critical region? Is the p-value higher or lower than your alpha? (75–150 words, or 1–2 paragraphs)
  • Note: Include your calculations. If your calculations are submitted separately, make note of where they can be found.
• 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. (75–150 words, or 1–2 paragraphs)
  • Is the observed test statistic in the critical region? Will the p-value be higher or lower than your alpha? (75–150 words, or 1–2 paragraphs)
  • Note: Include your calculations. If your calculations are submitted separately, make note of where they can be found.

Answer 1

The detailed calculation is shown below and the further explanation is attached here:

	X	(Xi-mean)	(Xi - Mean )^2
	29.7	2.98	8.8804
	24.5	-2.22	4.9284
	27.1	0.38	0.1444
	29.8	3.08	9.4864
	29.2	2.48	6.1504
	27	0.28	0.0784
	27.8	1.08	1.1664
	24.1	-2.62	6.8644
	29.3	2.58	6.6564
	25.9	-0.82	0.6724
	26.2	-0.52	0.2704
	24.5	-2.22	4.9284
	32.8	6.08	36.9664
	26.8	0.08	0.0064
	27.8	1.08	1.1664
	24	-2.72	7.3984
	23.6	-3.12	9.7344
	29.2	2.48	6.1504
	26.5	-0.22	0.0484
	27.7	0.98	0.9604
	27.1	0.38	0.1444
	23.7	-3.02	9.1204
	24.1	-2.62	6.8644
	27.2	0.48	0.2304
	25.9	-0.82	0.6724
	26.7	-0.02	0.0004
	27.8	1.08	1.1664
	27.3	0.58	0.3364
	27.6	0.88	0.7744
	22.8	-3.92	15.3664
	25.3	-1.42	2.0164
	26.6	-0.12	0.0144
	26.4	-0.32	0.1024
	27.1	0.38	0.1444
	26.1	-0.62	0.3844
Sum	935.2		149.996
Mean	26.72