A statistician for an automotive review magazine wants to determine whether there is a difference in the fuel efficiency of passenger vehicles between model years 2013 and 2018. To do this, he selects random makes and models of passenger vehicles and compares the fuel efficiency in miles per gallon of the 2018 model year and the 2013 model year. Suppose that data were collected for a random sample of 9 passenger vehicles, where each difference is calculated by subtracting the fuel efficiency in miles per gallon of the 2013 model year from the fuel efficiency in miles per gallon of the 2018 model year. Assume that the fuel efficiencies are normally distributed. The test statistic is t≈6.163, α=0.10, the corresponding rejection regions are t<−1.860 and t>1.860, the null hypothesis is H0:μd=0, and the alternative hypothesis is Ha:μd≠0. Which of the following statements are accurate for this hypothesis test in order to evaluate the claim that the true mean difference between the fuel efficiency of passenger vehicles from the 2018 model year and those from the 2013 model year is not equal to zero? A. Reject the null hypothesis that the true mean difference between the fuel efficiency of passenger vehicles from the 2018 model year and those from the 2013 model year is equal to zero. B. Fail to reject the null hypothesis that the true mean difference between the fuel efficiency of passenger vehicles from the 2018 model year and those from the 2013 model year is equal to zero. C. Based on the results of the hypothesis test, there is not enough evidence at the α=0.10 level of significance to suggest that the true mean difference between the fuel efficiency of passenger vehicles from the 2018 model year and those from the 2013 model year is not equal to zero. D. Based on the results of the hypothesis test, there is enough evidence at the α=0.10 level of significance to suggest that the true mean difference between the fuel efficiency of passenger vehicles from the 2018 model year and those from the 2013 model year is not equal to zero.
A statistician for an automotive review magazine wants to determine whether there is a difference in the fuel efficiency of passenger vehicles between model years 2013 and 2018. To do this, he selects random makes and models of passenger vehicles and compares the fuel efficiency in miles per gallon of the 2018 model year and the 2013 model year. Suppose that data were collected for a random sample of 9 passenger vehicles, where each difference is calculated by subtracting the fuel efficiency in miles per gallon of the 2013 model year from the fuel efficiency in miles per gallon of the 2018 model year. Assume that the fuel efficiencies are
Which of the following statements are accurate for this hypothesis test in order to evaluate the claim that the true mean difference between the fuel efficiency of passenger vehicles from the 2018 model year and those from the 2013 model year is not equal to zero?
A. Reject the null hypothesis that the true mean difference between the fuel efficiency of passenger vehicles from the 2018 model year and those from the 2013 model year is equal to zero.
B. Fail to reject the null hypothesis that the true mean difference between the fuel efficiency of passenger vehicles from the 2018 model year and those from the 2013 model year is equal to zero.
C. Based on the results of the hypothesis test, there is not enough evidence at the α=0.10 level of significance to suggest that the true mean difference between the fuel efficiency of passenger vehicles from the 2018 model year and those from the 2013 model year is not equal to zero.
D. Based on the results of the hypothesis test, there is enough evidence at the α=0.10 level of significance to suggest that the true mean difference between the fuel efficiency of passenger vehicles from the 2018 model year and those from the 2013 model year is not equal to zero.
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