Question

A consumer agency claims that the average fuel mileage of Sedan A exceeds that of Sedan B. To test this claim, a random sample of 14 Sedan A vehicles were tested and the sample mean fuel mileage was found to be 25.30 miles per gallon with a known population standard deviation of 1.45 miles per gallon. A random sample of 17 Sedan B vehicles also were tested and the sample mean fuel mileage was found to be 24.10 miles per gallon with a known population standard deviation of 1.90 miles per gallon. Use a 10% significance level and assume the fuel mileage values for each of the two populations of sedans are normally distributed.

**a.** Select the correct symbol to replace
"**?**" in the null hypothesis *H*_{0}:
*μ*_{A} − *μ*_{B}**?**
0

> | |

≥ | |

≤ | |

= | |

< |

**b.** Select the correct symbol to replace
"**?**" in the alternative hypothesis
*H*_{a}: *μ*_{A} −
*μ*_{B}**?** 0

< | |

≥ | |

> | |

≤ | |

≠ |

**c.** Compute the value of the test statistic used
to test the agency's claim.

**Do not round any intermediate calculations. Round your
answer to two decimal places. Enter a "−" sign directly before a
negative answer.**

Test statistic =

**d.** Determine the critical value used to test
the agency's claim.

**Enter your critical value to three decimal places. Enter
a "−" sign directly before a negative answer.**

Critical value =

**e. **Compute the *p*-value for
this hypothesis test.

**Use your rounded test statistic from Part c. Do
not round any other intermediate calculations. Round your final
answer to four decimal places.**

*p*-value =

**f.** Based on the above results, choose the
appropriate initial conclusion.

Do not reject the null hypothesis. | |

Reject the null hypothesis. |

**g.** Based on the claim and your initial
conclusion, choose the appropriate final conclusion.

Do not support the consumer agency's claim. | |

Support the consumer agency's claim. |

Answer #1

a)

Below are the null and alternative Hypothesis,

Null Hypothesis, H0: μ1 <= μ2

b)

Alternative Hypothesis, Ha: μ1 > μ2

c)

Pooled Variance

sp = sqrt(s1^2/n1 + s2^2/n2)

sp = sqrt(2.1025/14 + 3.61/17)

sp = 0.6021

Test statistic,

z = (x1bar - x2bar)/sp

z = (25.3 - 24.1)/0.6021

z = 1.99

d)

Rejection Region

This is right tailed test, for α = 0.1

Critical value of z is 1.282.

Hence reject H0 if z > 1.282

e)

P-value Approach

P-value = 0.0233

f)

As P-value < 0.1, reject the null hypothesis.

g)

Support the consumer agency's claim.

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