Chapter 13.4, Problem 41E

The shelf life of packaged food depends on many factors. Dry cereal is considered to be a moisture-sensitive product (no one likes soggy cereal!) with the shelf life determined primarily by moisture content. In a study of the shelf life of one particular brand of cereal, x = Time on shelf (days stored at 73°F and 50% relative humidity) and y = Moisture content (%) were recorded. The resulting data are from “Computer Simulation Speeds Shelf Life Assessments” (Package Engineering [1983]: 72–73).

1. a. Summary quantities are

   $\begin{array}{l}\Sigma x=269\Sigma y=51\Sigma xy=1081.5\\ \Sigma y^2=190.78\Sigma x^2=7745\end{array}$

   Find the equation of the estimated regression line for predicting moisture content from time on the shelf.

2. b. Does the simple linear regression model provide useful information for predicting moisture content from knowledge of shelf time?
3. c. Find a 95% interval for the moisture content of an individual box of cereal that has been on the shelf 30 days.
4. d. According to the article, taste tests indicate that this brand of cereal is unacceptably soggy when the moisture content exceeds 4.1. Based on your interval in Part (c), do you think that a box of cereal that has been on the shelf 30 days will be acceptable? Explain.