Question

# A machine is supposed to produce widgets with a diameter of 20mm or more. The standard...

A machine is supposed to produce widgets with a diameter of 20mm or more. The standard deviation of the population of widgets is known to be 5mm based on machine specifications. Quality Control takes a random sample of 25 widgets from the day's production and tests them.

Unknown to the company, the machine is not functioning correctly and produces widgets with an actual average diameter of 18mm. Assuming an alpha value of .05 is used, what is the probability of a Type II error? That is, how likely is it that the company will assume that the machine is still producing widgets with an average diameter of 20mm or more?

Use three decimal places in your calculations.

So the answer is: there is a 36.1% chance that the company assumes that the machine is still producing widgets with an average diameter of 20mm or more.

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