A food company produces a popular cream cheese for many years. From their experience, they know that
Question:
A food company produces a popular cream cheese for many years. From their experience, they know that the time period of its freshness (freshness time) can be well approximated by a normal distribution with mean 120 hours and variance 400 squared hours. Recently they have developed a new production and conservation method. They have measured the freshness time for 10 packages produced according to the new method, and the times in hours were 137, 116, 109, 124, 141, 133, 119, 139, 122, 131.
(a) Estimate the true mean freshness time of the cream cheese according to the new method.
(b) Test at a level of 5 whether there is evidence that on average the cream cheese produced by the new method is fresh for longer than 120 hours, taking the variance as unknown Interpret the result in a way understandable to a non statistician.
(c) Now imagine that it is of interest whether the variance of the freshness times is still 400 squared hours. Compute a 95 confidence interval for the variance Using the correspondence between tests and confidence intervals, test at 5 level whether 400 squared hours could be the true variance Interpret the result in a way understandable to a non statistician.
(d) The company needs to indicate a use by date on the packages, indicating for how long the customer can rely on the cheese being still fresh. Thinking in terms of hours after production, how could the company use the results above to decide what date to put there. (You can use your numerical results, explaining your reasoning, but you can also just explain in an abstract manner how the company can do that, in case you don't have numerical results).
Data Analysis and Decision Making
ISBN: 978-0538476126
4th edition
Authors: Christian Albright, Wayne Winston, Christopher Zappe