Question

A factory supplies parts for motorcycles. It produces a cylindrical engine part that is supposed to have a diameter of 6 centimetres. The factory’s quality control manager suspects that the machine producing the engine part is not working properly and that the mean diameter being produced is less than the correct size. To test if this belief is correct, a random sample of 40 parts is tested and measured. The sample mean diameter was found to be 5.9 cm. Assume that the diameter size of the engine part is normally distributed with a population standard deviation of 0.26 cm.

1. You were recently hired as a statistician working for the factory. Assist the quality control manager in performing a hypothesis test at a 3% level of significance to verify his belief. Display the six steps process (involving drawing the rejection region/s and determining the critical value/s for the decision rule) in performing the test.   
2. Calculate the p-value of the test above. Display working. State the decision rule should you want to use the p-value method in doing hypothesis testing.
3. Now that you have performed the test in part a), would you suggest to the manager to replace the machine? Why?   
4. Identify which one of these two types of error (Type I or Type II) you could make with the conclusion you made in part a). Briefly explain your selection

Answer 1

Let X : the diameter of cylindrical engine

Claim: the mean diameter of produced items is less than correct size

It may concluded at 3% level of significance that the machine not producing the engine of correct diameter

Thus the machine should be replacedreplaced.

The error that could possible in decision taken in part a is Type I error. That is concluding that machine is not working properly in fact it is working properly.

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