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Solve: Hypothesis Testing

Scenario: Your company must make a decision about a very large investment. An internal study shows that if demand for your product increases substantially from the current levels, new production lines must be set up to meet the demand at a reasonable cost and an acceptable quality level. Trying to meet the demand with current facilities will result in poor quality, loss of customer satisfaction and loss of business. But, if demand does not increase substantially the current production facilities will be adequate and the increased investment will not be required. In fact, if the investment is made when not required, the company's financial position will be harmed.
A consensus is reached that "substantial increase" means greater than 50 units.

Assume the data is ratio level. Sample size will be 225. We do not know the population standard deviation. Use an alpha of 1%. What are the hypotheses? What model (do we use T or Z to figure this out) applies and why?

Solution Preview

This is regarded as hypothesis testing about the population mean. We can set up the null hypothesis H0 and alternative hypothesis H1 as follows.

H0: mu=50,
H1: mu>50

Since we don't know the population ...

Solution Summary

This solution is comprised of a detailed response which clearly illustrates how to address this inquiry and formulate the necessary hypotheses for this question and compute the required values. This all completed in about 140 words.