Question

A public administrator for the Federal Aviation Administration, in light of terrorist | ||||

bombings and hijacking of airplanes, was concerned about how four different | ||||

methods of screening passengers affect traveler satisfaction. The four methods were | ||||

(1) no screen, (2) walk-through metal detector, (3) frisk search, and (4) handheld | ||||

metal detector. Random samples of traveler satisfaction were taken when the | ||||

travelers were screened by one of the four methods. The sample
sizes were n_{1}=2, n_{2}=3, |
||||

n_{3}=3, and n_{4}=2 for the four methods. The
results are below. Test the hypothesis |
||||

that the mean satisfaction values are the same for all four methods. Use the .05 | ||||

level of significance and assume normal distributions and equal variances for | ||||

each method. | ||||

No Screen | Walk-Through | Frisk | Hand-Held | |

8 | 10 | 11 | 16 | |

14 | 6 | 9 | 12 | |

18 | 8 | 7 | 18 | |

• State
H_{0} and H_{1}. |
||||

• Should
you reject or not reject H_{0}? (2 pts.)
Defend your answer. There |
||||

are 2 possible ways to do this. | ||||

• The three means (are / are not) the same. |

Answer #1

Here we'll be applying analysis of variance. The result is below

Here p-value is > than the significance level 0.05. Thus we fail to reject the null hypothesis.

Also, the F-statistic follows an F-distribution with 3 and 8 degrees of freedom. Thus the critical value at the significance level 0.05 is 4.066. But the F-statistic is less than the critical value thus we fail to reject the null hypothesis.

Thus the 4 means are the same.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 11 minutes ago

asked 13 minutes ago

asked 14 minutes ago

asked 47 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago