One criterion used to evaluate employees in the assembly section of a large fact

Question

One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below. Set up and conduct a test to verify if there is a relationship between years of training and performance (defect rates).

Explanation / Answer

Null hypothesis: Assumes that there is no association between the two variables.

Alternative hypothesis: Assumes that there is an association between the two variables.

R codes :
>x=matrix(c(6,9,9,9,19,23,7,8,10),nrow=3,byrow=T)
> chisq.test(x)

OUTPUT:

Pearson's Chi-squared test

data: x
X-squared = 1.351, df = 4, p-value = 0.8527

Here, since p-value > 0.05, we accept the null hypothesis of independence at 5% level of significance and conclude that there is no significant relationship between years of training and performance.

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