[3]. As part of the investigation of the collapse of the roof of a building, a t

Question

[3]. As part of the investigation of the collapse of the roof of a building, a testing laboratory is given all the available bolts that connect the steel structure at 3 different positions on the roof. The forces required to shear each of these bolts (coded values) are as follows Position 1: 90 82 79 98 83 91 Position 2: 105 89 93 104 89 95 86 Position 3: 83 89 80 94 You are asked to perform an analysis of variance to test, at 0.05 level of sig nificance, whether the differences among sample means at the 3 positions are significant. (a) (10 Points) Write down your null and alternative hypotheses. (b) (20 Points) Perform the analysis of variance (ANOVA) calculations and com plete the following table with results from your calculations. You must show details of your calculations, to the extend possible, to earn credit. Simply writing answers to fill the table will not be credited (c) (10 Points) Clearly state your decision (or conclusion) based on the analysis. Source of Variation Degree of Freedom Sum of Mean Squares 234 938 Square Positions Error Total

Explanation / Answer

Step 1

null, Ho: µ1 =µ2 =µ3

alternative, H1: atleast one mean is diffrent among them

Step 2

Degrees of freedom between = 3 - 1 = 3 - 1 = 2

Degrees of freedom Within = n - k = 17 - 3 = 14

Degrees of freedom Total F( k-1,n - k,) at 0.05 is = F Crit = 3.739

Step 3

Grand Mean = G / N = 90

SST = ( Xi - GrandMean)^2 = 938.00  

SS Within = (Xi - Mean of Xi ) ^2 =234.45

SS Between = 703.55

Step 4

Mean Square Between = SS Between / df Between = 117.226

Mean Square Within = SS Within / df Within = 50.253

Step 5

F Cal = MS Between / Ms Within = 2.33

We got |F cal| = 2.33 & |F Crit| =3.739

MAKE DECISION

Hence Value of |F cal| < |F Crit|and Here We Accept Ho

Mean n Std. Dev 87.2 6 7.08 Position 1 94.4 7 7.48 Position 2 86.5 4 6.24 Position 3 90.0 17 7.66 Total

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