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. Inspectors randomly select 16 boxes of new and old packages, and report the temperatures in degrees Celsius 24 hours after they are sealed for shipment. A portion of the data is shown in the accompanying table. Assume that the two samples are drawn independently from normally distributed populations. (You may find it useful to reference the appropriate table: chi-square table or F table)
| New Package | Old Package |
|---|---|
| 3.98 | 5.79 |
| 4.99 | 6.42 |
| 5.15 | 4.88 |
| 5.23 | 4.02 |
| 4.77 | 4.76 |
| 5.21 | 5.08 |
| 5.51 | 4.58 |
| 4.95 | 5.44 |
| 5.52 | 3.98 |
| 5.52 | 5.79 |
| 4.98 | 5.77 |
| 4.28 | 4.30 |
| 5.12 | 6.41 |
| 5.08 | 4.55 |
| 5.86 | 6.02 |
| 4.95 | 5.95 |
Click here for the Excel Data File
a. Let Old Package represent population 1 and New Package represent population 2. Select the hypotheses to test whether the new packaging material reduces the variation of temperatures in the box.
multiple choice 1
H0: ?12 / ?22 = 1, HA: ?12 / ?22 ? 1
H0: ?12 / ?22 ? 1, HA: ?12 / ?22 > 1
H0: ?12 / ?22 ? 1, HA: ?12 / ?22 < 1
b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)