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

Part 1: Sample Mean, Standard Deviation, and Confidence Interval

Part 2: Hypothesis Testing: Two-Tail Test and One-Tail Test

In these testing Part 1 showed that the company's number are showing up less than what they are implying....

Part 2 testing is showing that the claim is true.

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

• What conclusions did you reach? What did you learn about the situation by using each method? Did one method offer more conclusive proof than another? (150–225 words, or 2–3 paragraphs)
• Based on your results, do you support the company’s claim that their minivans get 28 miles per gallon? (75 words, or 1 paragraph)
• Summarize the details of your test methods and the results from each statistical method you used. Explain the findings so that executives from both the agency and the company can understand your conclusion. (150–225 words, or 2–3 paragraphs)
• Finally, present recommendations for actions that the company might take to use your findings to better serve their customers in the future. (75 words, or 1 paragraph)

Answer 1

The 95% confidence interval will be:

= x ± t*(s/√n)

= 26.72 ± 2.03*(2.10039/√35)

= (25.9985, 27.4415)

The 95% confidence interval that the highway mileage for all minivans is between 25.9985 and 27.4415.

Since the confidence interval does not contain 28, we cannot conclude that minivans get 28 miles per gallon on the highway.

The hypothesis being tested is:

H₀: µ = 28

H_a: µ ≠ 28

The test statistic, t = (x - µ)/s/√n

t = (26.72 - 28)/2.10039/√35

t = -3.605

The p-value is 0.0010.

Since the p-value (0.0010) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we cannot conclude that minivans get 28 miles per gallon on the highway.

Please give me a thumbs-up if this helps you out. Thank you!