Suppose a new production method will be implemented if a hypothesis test supports the conclusion that the new method reduces the mean operating cost per hour. a. State the appropriate null and alternative hypotheses if the mean cost for the current production method is 215 per hour.

b. What is the Type I error in this situation? What are the consequences of making this error?

c. What is the Type II error in this situation? What are the consequences of making this error?

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a.

The claim is that the new production method reduces the mean operating cost per hour.

If we are comparing the average production cost of the new production method (μ₁) vs the average production cost of the old production method (μ₂), the hypotheses are:

H₀: μ₁ ≥ μ₂

H₁: μ₁ < μ₂

b.

The type I error occurs when you reject the null hypothesis when the hypothesis is true.

In this case, a true null hypothesis means that the average operating cost/hr of the new production method is at least the same as the average operating cost/hr of the old production method.

If the hypothesis is rejected, this means that the company will assume that the average costs/hr will be reduced with the new production method. This can lead them to the decision of changing the production method and thus having equal or greater operating costs/hr.

c.

The type II error occurs when you fail to reject the null hypothesis when the hypothesis is false.

If the null hypothesis is false, this means that the alternative hypothesis is true. In this case, it means that the average operating cost/hr of the new production method is less than the average operating costs/hr of the old production method.

Failing to reject this false null hypothesis will mean that the company will assume that the new method costs the same or more like the old method and thus will not change methods although, in reality, they would spend less with the new one.

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