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 n1=2, n2=3,
n3=3, and n4=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 H0 and H1.
• Should you reject or not reject H0? (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.