1. A supermarket manager is examining whether a new plastic bagging configuration in the produce area might make it more efficient for customers who are bagging their own fruits and vegetables. She observes a sample of customers using the new system and a sample of customers using the standard system, and she notes how many seconds it took each of them to unroll and open the plastic bag in preparation for bagging the veg- gies. The data are in file XR11098. Considering these as data from independent samples, use the 0.025 level of significance in examining whether the population mean for the new bagging system might be less than that for the conventional system. Identify and interpret  the p-value for the  test.

2. A company that makes an athletic shoe   designed  for basketball has stated in its advertisements that  the  shoe increases the jumping ability of players who wear it. The general manager of a professional team has conducted a test in which each player's vertical leap is measured with the current shoe versus the new model, with the data as listed in file XR11099. At the 0.05 level of significance, evaluate the claim that has been made by the shoe com- pany. Identify and interpret the p-value for the test.