Question

Two processes are used to produce forgings used in an aircraft wing assembly. Of 200 forgings selected from process 1, 10 do not conform to the strength specifications, whereas of 300 forgings selected from process 2, 20 are nonconforming. Test the hypothesis that the two processes have identical fractions nonconforming. Use ? = 0.05. State your hypothesis and test statistic.

Answer 1

Here we want to test the hypothesis that the two processes have identical fractions nonconforming

Let's write null and the alternative hypothesis.

Let's used minitab:

Step 1: Click on Stat >>> Basic Statistics >>>2 Proportions...

Step 2: Select Summarized data

Fill the given information

Look the following picture ...

Then click on Option:

Look the following image:

Then click on OK again click on Ok

So we get the following output

From the above output

z = 0.-79 , p-value = 0.429

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.429 > 0.05 so we used 2nd rule.

That is we fail to reject null hypothesis

Conclusion: At 5% level of significance there are not sufficient evidence to conclude that the two processes have not identical fractions nonconforming.