Question

Many drivers of cars that can run on regular gas actually buy premium in the belief that they will get better gas mileage. To test that belief, we use 10 cars from a company fleet in which all the cars run on regular gas. Each car is filled first with either regular or premium gasoline, decided by a coin toss, and the mileage for that tankful is recorded. Then the mileage is recorded again for the same car for tankful of the other kind of gasoline. We don't let the drivers know about this experiment. Here are the results (in miles per gallon).

Car# : 1 2 3 4 5 6 7 8 9 10

regular: 16 20 21 22 23 22 27 25 27 28

Premium:19 22 24 24 25 25 26 26 28 32

Is there evidence that cars get significantly better fuel economy with premium gasoline? Use 5% level of significance.

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Answer #1

The objective of the study is to test and determine whether the cars get significantly better fuel economy with premium gasoline.

The null and alternative hypothesis is

Level of significance = 0.05

Test statistic is

Regular | Premium | Difference |

16 | 19 | -3 |

20 | 22 | -2 |

21 | 24 | -3 |

22 | 24 | -2 |

23 | 25 | -2 |

22 | 25 | -3 |

27 | 26 | 1 |

25 | 26 | -1 |

27 | 28 | -1 |

28 | 32 | -4 |

Total | -20 |

Sample size = n = 10

Sample mean of difference = = - 2

Sample standard deviation = = 1.414214

Degrees of freedom = n - 1 = 10 - 1 = 9

Critical value = 1.833 ( Using t table)

| t | > critical value we reject null hypothesis.

Conclusion: There is sufficient evidence that there evidence that cars get significantly better fuel economy with premium gasoline.

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