Question

Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 15 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 5 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. What is the rejection region for the ANOVA test using an arbitrary level of significance .

Answer 1

There are k = 3 methods that are present for assembling the products. A total of N = 15 employees have been assigned randomly to check for the number of units that are correctly assembled by each method.

For an ANOVA test, F-statistic is used. The statistic is calculated as the ratio of Mean Squares Between Groups and Mean Square Within Groups. The degrees of freedom for Within Groups is df1 = k-1 = 3-2 = 2. The degrees of freedom for Between Groups is df2 = N-k = 15-3 = 12.

We can keep a significance level that is commonly used. This significance level is 0.05.

Now using the F-table, the significance level of 0.05, and the degrees of freedom (2, 12), we can get the critical value. This significance level is 3.8853.

Therefore, the rejection region will be for F<3.8853 and also for the negative side i.e. for F>-3.8853.

To summarize, the rejection region for the test becomes -3.8853 < F < 3.8853.