Question

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 41 of its new minivans to test their highway mileage. The company claims that its minivans get 28 miles per gallon on the highway. Your test results show a sample mean of 26.7 and a sample standard deviation of 4.2.

Part 1 (Confidence Interval):

Calculate a 95% confidence interval around your sample mean.

Is the claimed mean inside your confidence interval?

What does your result mean, in terms of the company's claim?

Answer 1

Confidence InterVal :

Mean = 26.7 , SD = 4.2, Sample (n) = 41 , Z value (95% condidence interval) = 1.96

Upper Limit = 26.7 + 1.96 x 4.2 / (41)^0.5 = 26.7 + 1.28 = 27.98 (almost 28)

Lower Limit = 26.7 + 1.96 x 4.2 / (41)^0.5 = 26.7 - 1.28 = 25.41

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Claim is not inside the interval or may be at the very extreme range on right side of distribution , but no sufficient evident that it is well inside the range. So, we can assume it is outside,may be for some cases, result may show 28, but most of the cases this is not true figure.

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Based on the sample collected , Company's claim is not true. Very few % of vehicle might have shown the desired performance, but majority falls to achieve the same.

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Plz provide feedback on final Ans.........Plz get back for any clarification or question.......All the best