STATISTICS FOR ECONOMISTS Homework 6 Topic 4: Estimation using Confidence Interval Based on Chapter 8 of Berenson et al. (2015), Basic Business Statistics: Concepts and Applications, 13th Edition, Pearson. 1. A sample of size 16 from a normal population with known variance (25) yielded a sample mean equal to 14.5. Within what interval can we be 90% confident that the population mean lies? 2. Suppose that from a random of 10 heights we find that the mean = 171.2 cm and the standard deviation = 10. Then a 95% confidence interval for the population mean height is (assume that height is normally distributed). 3. Suppose that we check for clarity in 50 locations in Lake Tahoe and discover that the average depth of clarity of the lake is 14 feet. Suppose that we know that the standard deviation for the entire lake's depth is 2 feet. What can we conclude about the average clarity of the lake with a 95% confidence level? 4. Suppose that we conduct a survey of 19 millionaires to find out what percent of their income the average millionaire donates to charity. We discover that the mean percent is 15 with a standard deviation of 5 percent. Find a 95% confidence interval for the mean percent. Assume that the distribution of charity percent is approximately normal. 5. Determine the margin of error for a confidence interval estimate for the population mean of a normal distribution given the following information a. confidence level = 0.98, n = 13, s = 14.37 b. confidence level = 0.99, n = 16, 6= 3.47 c. confidence level = 0.98, standard error of the mean (Ox ) = 2.356