Company B is investigating the effect of machine configuration on the number of

Question

Company B is investigating the effect of machine configuration on the number of widgets produced per minute. Concerned that they would not have a large enough sample, they decide to collect data across five different operators. While they know that differences in the operators are also likely to have an effect, they are not interested in this effect and select a design that allows them to investigate the effect of the machine configuration while controlling for differences in operators. They collect the following data Marginal Means 6.8 5.2 3.6 3.8 Grand Mean: 4.85 Marginal Variances 3.2 5.7 1.8 2.2 Operator Machine Configuration 10 6 6 Marginal Means Marginal Variances 4.75 4.75 2.75 4.7 2.3 2.3 4.9 2.0

Explanation / Answer

Solution:

If the sum of squares fir the operators is 36.3 and Sum of square for the error is 15.3. Then F test statistic is:

F test = Mean sum of square/ Mean sum of square for Error

Since, Mean sum of square= Sum of square/df

=36.3/5-1=36.3/4=9.075

And Mean sum of square for Error=15.3/15 =1.02

Therefore, F test = 9.075/1.02=8.89

And Critical value of F test=3.804 (using table F4,15 =3.804)

Cheers!!

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