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Fuel economy. Although the Environmental Protection Agency (EPA) establishes the tests to determine the fuel economy of new cars, it often does not perform them. Instead, the test protocols are given to the e. car companies, and the companies perform the tests themselves. To keep the industry honest, the EPA runs some spot checks each year. Recently, the EPA announced that Hyundai and Kia must lower their fuel economy estimates for many of their models.9 Here are some city miles per gallon (mpg) values for one of the models the EPA investigated: Iin MILEAGE 78. 28.0 25.7 25.8 28.0 28.5 29.8 30.2 30.4 26.9 28.3 29.8 27.2 26.7 27.7 29.5 28.0 Give a 95% confidence interval for ?, the mean city mpg for this model.

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Answer:

95% confidence interval for the mean city mpg for the model is 28.156±0.791 that is (27.365,28.947)

Step-by-step explanation

Confidence Interval can be calculated using M±ME where

  • M is the mean miles per gallon (mpg) values for the models the EPA investigated
  • ME is the margin of error from the mean

And margin of error (ME) from the mean can be calculated using the formula

ME=[tex]\frac{t*s}{\sqrt{N} }[/tex] where

  • t is the corresponding statistic in the 95% confidence level
  • s is the standard deviation of the sample
  • N is the sample size (16)

mean miles per gallon (mpg) values can be calculated dividing the sum of the samples by sample size, which yields 28.156

standard deviation of the sample distribution can be calculated by adding square differences from the mean and dividing by sample size, which yields 1.437

statistic in the 95% confidence level with 15 degrees of freedom is 2.131

Then ME=[tex]\frac{2.131*1.437}{\sqrt{15} }[/tex] ≈ 0.791

95% confidence interval would be 28.156±0.791 that is (27.365,28.947)

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