We would like to conduct a hypothesis test to check whether five technicians gav

Question

We would like to conduct a hypothesis test to check whether five technicians gave measure of product yield. With the initial da ta collection of five runs per each technician, data is summarized below. The descriptive statistics and ANOVA result of these data are: Variable Technicians Mean StDev Yield I 90.38 3.02 II 91.240 1.707 III 92.74 3.50 IV 94.76 3.40 V 94.70 2.68 Analysis of variance Source DF Adj SS Adj MS F P Technicians 4 78.69 19.673 2.29 0.096 Error 20 171.98 8.599 Total 24 250.68 If we wish to able to detect a maximum difference in mean measure of product yield of 4 units with a probability of at least 0.85, what sample size should be used?

Explanation / Answer

Here we have given that the one way ANOVA output.

The problem has five levels and to test means at each level and now we have to find sample size.

Given that,

maximum difference = 4

probability = 0.85

Assume alpha = level of significance = 0.05

Standard deviation = sqrt(MSE) = sqrt(8.599) = 2.9324

Then we can find sample size for one way ANOVA using MINITAB.

steps :

Open MINITAB sheet --> Stat --> Power and Sample size --> One way ANOVA --> Number of levels : 5 --> Specify values for any two of the following --> Values of the maximum difference between means : 4 --> Power values : 0.85 --> Standard deviation : 2.9324 --> Options --> Significance level : 0.05 --> ok --> ok

Output :

Power and Sample Size

One-way ANOVA

Alpha = 0.05 Assumed standard deviation = 2.9324 Number of Levels = 5

SS Sample Target Maximum
Means Size Power Actual Power Difference
8 16 0.85 0.865683 4

The sample size is for each level.

Therefore sample size is 16.

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