Discussion:
1. Suppose you are sampling from a population with mean µ = 1,065 and standard deviation σ = 500. The sample size is n = 100. What are the expected value and the variance of the sample mean X? Show
2. Suppose a new estimator for the population mean is discovered. The new estimator is unbiased and has a variance equal to σ^2 / n^2 . Discuss the merits of the new estimator compared with the sample mean
3. Thomas Stanley, who surveyed 200 millionaires in the United States for his book The Millionaire Mind, found that those in that bracket had an average net worth of $9.2 million. The sample variance was 1.3 million $^2. Assuming that the surveyed subjects are a random sample of U.S. millionaires, give a 99% confidence interval for the average net worth of U.S. millionaires.
4. Use the following random sample of suitcase prices to construct a 90% confidence interval for the average suitcase price. Show and explain your answer
$285, $110, $495, $119, $125, $250, $320