EBook Three different methods for assembling a product were...

eBook Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: SST=10,810; SSTR =4,520. a. Set up the ANOVA table for this problem (to 2 decimals, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value (to 4 decimals) Treatments Error Total b.Use $alpha = .05$ to test for any significant difference in the means for the three assembly methods. Calculate the value of the test statistic (to 2 decimals).

Transcript

00:01 So we're running an anova here.

00:03 So there are three different methods, k is three, for an assembly.

00:06 And this is the methods for assembling a product, which are proposed by an industrial engineer.

00:13 And so to investigate the number of units assembled correctly for each method, a total of n equals 30 employees were randomly selected and randomly assigned to the three different methods of assembly.

00:25 And so that means each group had a total of 10 workers in each.

00:29 So now the number of units assembled correctly was recorded and we're going to do an anova, a one -way anova, analysis of variance to the dataset.

00:43 And then we had some results that were given to us.

00:45 We're given that the total sum of squares is 10 ,810.

00:51 And the sum of squares of the treatment is 4540.

01:09 And we're given the, there's some stuff that was incorrectly placed in here.

01:16 So we're going to correct it and then make our, correct it and it'll be wonderful.

01:21 So let's go and do this.

01:22 So first off the treatment sum of squares should be 4540.

01:28 So this should be 4540.

01:32 And then the total sum of squares is 10 ,810.

01:36 And then something about the sum of squares, one of the beautiful things about it is that they equal the treatment sum of squares and the residual sum or the error sum of squares add together to get the total.

01:49 So let me put that as an equation.

01:51 Sst equals sstr plus sse.

01:59 So if we want to find the treatment, or the error sum of squares, we just subtract the treatment sum of squares from both sides and then we'll be good to go.

02:09 So we just manipulate the equation a little bit.

02:11 We get that.

02:12 So we take the difference of 10 ,810 and 4540 and we get 6270.

02:20 These are the correct degrees of freedom.

02:22 Treatments is two because k minus one degrees of freedom is the degrees of freedom for the treatment.

02:26 So three minus one is two.

02:28 For the error, it's big n minus k.

02:32 So 30 minus three is 27.

02:34 And then this would be 29.

02:38 And the reason it'd be 29 is because that is big n minus one.

02:42 Big n is the total number in the example.

02:44 All right, now the mean square of the treatment is equal to the sum of squares of the treatment divided by the degrees of freedom of the treatment.

02:59 So 4540 divided by two...

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