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

For t statistic

Mean of first machine xM = 6.8

Mean for other machines X0 = (5.2 + 3.6 + 3.8)/3 = 4.2

Variance of Firsr machine sM2 = 3.2

Variance of other machine so2 = 3.314

pooled Variance sp2 = [4 * 3.2+ 14 * 3.314]/ 18 = 3.2886

Pooled standard deviation sp = sqrt(3.2886) = 1.8134

Test Static

t = (6.8 - 4.2)/ 1.8134 * sqrt (1/5 + 1/15) = 2.6/ 0.9457 = 2.75

SO test statistic

t = 2.75

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