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Solve: Hypothesis Testing

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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?

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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.

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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 ...

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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