2. 4.146 Weight Loss Program. Suppose that a weight loss company advertises that people using its program lose an average of 8 pounds the first month, and that the Federal Trade Commission is gathering evidence to see if this advertising claim is accurate. If the FTC finds evidence that the average is less than 8 pounds, the agency will file a lawsuit against the company for false advertising. a. What are the null and alternative hypotheses? b. Suppose that the FTC gathers information from a very large random sample of patrons and finds that the average weight loss during the first month in the program is =7.9 pounds with a p-value for this result of 0.006. Are the results statistically significant at the a=0.01 level? c. If any error were to occur in the decision to reject or fail to reject, would it be a Type I error or a Type II error? d. Do you think the results of the test are practically significant? In other words, do you think patrons of the weight loss program will care that the average is 7.9 pounds lost rather than 8.0 pounds lost? Discuss the difference between practical significance and statistical significance in this context. In each of the following set circumstances described, indicate whether a researcher would want to use a small or a relatively large significance level a to address the concern. Briefly explain your reasoning. a. A new selective herbicide is being tested to kill weeds growing in crops. It is believed to have similar effectiveness to other selective herbicides but the cost is about 10% lower. The hypotheses are: Ho: The new herbicide is safe for human consumption Ha: The new herbicide is unsafe for human consumption b. A new drug to treat an aggressive form of cancer is in clinical trials, and is believed to be able to stop the growth of a tumor in situations where no other effective treatment has been found. The hypotheses are: Ho: The new drug is free of serious long-term side effects Ha: The new drug has some serious long-term side effects