yifuli Ledciter and Hogg report that a civil engineer wishes to compare the stre

Question

yifuli Ledciter and Hogg report that a civil engineer wishes to compare the strengths of three different types of beams, one (A) made of steel and two (B and C) made of different more expensive alloys. A certain deflection (in units of 0.001 inch) was measured ofr each beam when submitted to a given ofrce; thus, a small deflection would indicate a beam of great strength. The order statistics ofr the three samples, of respective sizes J_1 = 8, k_2 = 6, and j_2 = 6, are as ofllows: A: 79 82 83 84 85 86 86 97 B: 74 75 76 77 78 82 C: 77 78 79 79 79 82 Use these data, alpha = 0.05, and the F lest to test the equality of the three means. Use Tukey s procedure to identify difference in true average deflection strengths among the three different types of beams. Hint: Q0.06,3.17 = 3.63 A researcher wishes to see whether the type of gasoline used and the type of automobile driven have any effect on gasoline consumption. Two types of gasoline, regular and high-octane, will be used, and two types of automobiles, two-wheel-and ofur-wheel drive, will be used in each group. There will be two automobiles in each group, ofr a total of eight automobiles used. After constructing an ANOVA table, test the hypotheses H_OAB: no interaction, H_OA; no row effect, and H_OB; no column effect, each at the 5% significance level.

Explanation / Answer

Sol)

H0: All three groups means are equal

H1: Atleast one group is not same

Level of significance: 5%

Test statistics:

We use One Way ANOVA

From Excel

Conclusion:

P=0.000153 which is less than 0.05 we reject Ho. Hence the result is significant.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance A 8 672 84 6.857143 B 6 462 77 8 C 6 474 79 2.8 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 184.8 2 92.4 15.4 0.000153 3.591531 Within Groups 102 17 6 Total 286.8 19

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