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Engineering Probability and Inference Homework 3 A consumer product-testing organization wanted to compare the annual power consumption for five different brands of dehumidifier

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Engineering Probability and Inference Homework 3

1. A consumer product-testing organization wanted to compare the annual power consumption for five different brands of dehumidifier. The resulting power consumption data is below:

Brand	Power Consumption
1	685		792	838	875
2	722		806	893	953
3	733		802	880	941
4	811		888	952	1005
5	828		920	978	1023

 

1. Do the data provide sufficient evidence to indicate a difference in power consumption among the five brands? Use a significance level of 0.05. Construct the full ANOVA table.
2. User Tukey’s W Procedure to determine which location means differ (if any) from which others, using a 0.05 level of significance.

 

 

2. A study was carried out to compare the writing lifetimes of four premium brands of pens. Lifetimes are given below for the pens.

 

Brand of Pen
1	709,  559,  713,   726,  660,   545
2	668,  685,  722,  740,  692,  720
3	659,  685,  666,  684,  678,  750
4	789,  750,  804,  766,  786,  733

 

1. Use a 0.01 significance level to test if the four brands have the same mean lifetimes. Construct the full ANOVA table.
2. If we consider brand 1 as a control, use Dunnett’s procedure to test if the other three brands each differ from brand 1. Use a significance level of 0.01.

 

 

3. Observations on axial stiffness from a study of metal-plate connected trusses were taken on five different plate lengths. Use the Kruskal-Wallis test and a significance level of 0.01 to test if the axial stiffness depends on plate length. Then use the Kruskal-Wallis Multiple-Comparison procedure to test for differences in the paired mean ranks. Use a 0.01 significance level for these comparisons as well.

 

Plate Length	Axial Stiffness
4”	309.2	309.7	311.0	316.8	326.5	326.5	409.5
6”	331.0	347.2	348.9	361.0	381.7	402.1	404.5
8”	351.0	357.1	366.2	367.3	382.0	392.4	409.9
10”	346.7	362.6	384.2	410.6	433.1	452.9	461.4
12”	407.4	410.7	419.9	441.2	441.8	465.8	473.4