A variety of packaging solutions exist for products that must be kept within a specific temperature range. Cold chain distribution is particularly useful in the food and pharmaceutical industries. A packaging company is trying out a new packaging material that might reduce the variation of temperatures in the box. It is believed that the temperature in the box follows a normal distribution with both packaging materials. Inspectors randomly select 16 boxes of new and old packages, 24 hours after they are sealed for shipment, and report the temperatures in degrees Celsius. A portion of the data is shown in the accompanying table. Assume that the two samples are drawn independently from normally distributed populations.
New Package...............Old Package
3.98....................................5.79
4.99....................................6.42
⋮.............................................⋮
4.95....................................5.95
a. State the appropriate hypotheses to test whether the new packaging material reduces the variation of temperatures in the box.
b. Use Excel's F.TEST function to calculate the p-value.
c. Make a conclusion at the 5% significance level.