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?   Defend your answer. There
are 2 possible ways to do this.
• The three means (are / are not) the same.

Answer 1

Result:

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

Ho: µ1= µ2= µ3= µ4

H1: At least one of the mean is different from the others

Calculated F=2.2803

Table value of F with (DF1=3, DF2=7 ) =4.35

Calculated F=2.2803 < 4.35 the table value

The null hypothesis is not rejected. ( we do not reject H0)

The data indicate there is no difference among the four groups

• The three means (are ) the same.

ANOVA: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
No Screen	3	40	13.33333333	25.3333
Walk-Through	3	24	8	4.0000
Frisk	3	27	9	4.0000
Hand-Held	2	28	14	8.0000
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	72.9697	3	24.3232	2.2803	0.1664	4.3468
Within Groups	74.6667	7	10.6667
Total	147.6364	10
			Level of significance	0.05