Ledolter and Hogg report that a civil engineer wishes to compare the strengths o

Question

Ledolter and Hogg report that a civil engineer wishes to compare the strengths of three different types of beams, one (A) made ot steel and wo and more expensive alloys. A certain deflection (in units of 0.001 inch ) for each beam when submitted to a given force; thus, a small deflection would indicate a beam of great strength. The order statistics for the three samples, o respective sizes J_1 = 8,j_2 = 6, and J_3 = 6, are as follows: Use these data, alpha = 0.05, and the F test to test the equality of the three means Use Tukey s procedure to identify differences in true average deflection strengths among the three different types of beams.

Explanation / Answer

Sol)

Ho: All the three groups means are equal

H1: Atleast one group is not same

Level of significance is 5%

Test Statistics:

We use one way anova

From Excel

Conclusion:

F cal=15.4

P value=0.000153

P< Alpha we rehect the null hypothesis.

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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