Please hand in to the economics office (AS2 -L6)

 • Please hand in to the economics office (AS2 -L6) • Late assignments will not be accepted. • Show your work to get full credit. • Carry through fractions or exact decimals when possible, or round to four decimal places. Please round final answers to four decimal places. 1. NCT 7.7 Suppose that x1 and x2 are random samples of observations from a population with mean and variance s2. Consider the following three point estimators, X, Y , and Z of : X =12x1 + 12x2 Y =14x1 + 34x2 Z =13x1 + 23x2 (a) Show that all three estimators are unbiased (b) Which of these estimators is the most efficient? (c) Find the relative efficiency of X with respect to each of the two other estimators 2. NCT 7.13 A personnel manager has found that historically, the scores on aptitude tests given to applicants for entry-level positions follow a normal distribution with a standard deviation of 32.4 points. A random sample of nine test scores from the current group of applicants had a mean score of 187.9 points. Find an 80% confidence interval for the population mean score of the current group of applicants. 3. NCT 7.47 The quality control manager of a chemical company randomly sampled twenty 100-pound bags of fertilizer to estimate the variance in the pounds of impurities. The sample variance was found to be 6.62. Find a 95% confidence interval for the population variance in the pounds of impurities. What assumption, if any, did we make about the underlying population distribution? 4. NCT 7.69 A politician wants to estimate the proportion of constituents favoring a controversial piece of proposed legislation. Suppose that a 99% confidence interval that extends at most 0.05 on each side of the sample proportion is required.