1. Imagine that there are 100 different researchers each studying the sleeping habits of college freshmen. Each researcher takes a random sample of size 50 from the same population of freshmen. Each researcher is trying to estimate the mean hours of sleep that freshmen get at night, and each one constructs a 95% confidence interval for the mean. Approximately how many of these 100 confidence intervals will NOT capture the true mean? 2. Nana Akosua Owusu – Ansah, a financial manageress for a company is considering two competing investment proposals. For each of these proposals, she has carried out an analysis in which she has determined various net profit figures and has assigned subjective probabilities to the realization of these returns. For proposal A, her analysis shows net profits of GH? 20,000.00, GH? 30,000.00 or GH? 50,000.00 with respective probabilities 0.2, 0.4 and 0.4. For proposal B, she concludes that there is a 50% chance of successful investment, estimated as producing net profits of GH? 100,000.00, and of an unsuccessful investment, estimated as a break – even situation involving GH? 0.00 of net profit. Assuming that each proposal requires the same Ghana cedi investment, which of the two proposals is preferable solely from the standpoint of expected monetary return?