1. A nutritionist has noticed a FoodFarm ad stat- ing the company's peanut butter contains less fat than that produced by a major competitor. She purchases 11 8-ounce jars of each brand and measures the fat content of each. The 11 FoodFarm jars had an aver- age of 31.3 grams of fat, with a standard deviation of 2.1 grams. The 11 jars from the other company had an average of 33.2 grams of fat, with a standard deviation of 1.8 grams. Assuming normal populations with equal standard deviations, use the 0.05 level of significance in examining whether FoodFarm's ad claim could be valid. What is the most accurate statement that could be made about the p-value for this test?
2. A study published in the Archives of Internal Medicine examined the prevalence of so-called "difficult" patients who ask for unneeded prescriptions, unnecessarily complain, or otherwise cause extraordinary frustrations for their medical provider. Researchers found the mean age of doctors having the greatest problems with difficult patients was 41, while the mean age of doctors having the least problems with difficult patients was 46. Assume that data file XR11012 contains the ages for doctors in each of these patient-difficulty samples. In a suitable one-tail test at the 0.01 level, was the mean age for doctors having the greatest problems with difficult patients significantly less than that for those having the least problems with difficult patients? Identify and interpret the p-value for the test.
Source: Rita Rubin, "‘Difficult Patients Can Test Doctors' Patience," USA Today, February 24, 2009, p. 5D.