Task:
You decide to measure the time between equipment malfunctions over a one-year period. Over that time you measured 40 electronic products. You made 850 observations with a mean time between equipment failures of 550.35 hours, and a sample standard deviation of 207 hours.
Your company supplies the electronic product to another company as a component to their product. You guarantee an average time between malfunctions of 600 or more hours.
Calculate a 99% confidence interval estimate for the mean time between malfunctions for all electronics of this type then interpret the results to assess whether your company will have a problem with this guarantee. Why?
a) Describe the two assumptions needed for the confidence interval statement to be valid
b) For each assumption, give an example of what could go wrong if it were not satisfied
c) How does the central limit theorem help satisfy one of these assumptions?