. Figure 6.5 (page 339) demonstrates the behavior of a confidence interval in repeated sampling by showing the results of 25 samples from the same population.Now you will do a similar demonstration, though in an artificial setting. Suppose that the attorney fees for Chapter 7 consumer bankruptcies for the population of Chapter 7 consumer bankruptcies follow the uniform distribution between $250 and $1750. Then the mean attorney fees is Î¼ = 1000 and the standard deviation is Ïƒ = 433.
(a) Simulate the drawing of 25 SRSs of size n = 100 from this population.
(b) For calculating the confidence intervals, you are willing to assume that the sample means are approximately Normal. Explain
why this is a reasonable assumption.
(c) The 50% confidence interval for the population mean Î¼ has the form x Â±m. What is the margin of error m? (Use 433 for the standard deviation.)
(d) Use your software to calculate the 50% confidence interval for Î¼ for each of your 25 samples. Verify the computerâ€™s calculations by checking the interval given for the first sample against your result in (b). Use the x reported by the software.
(e) How many of the 25 confidence intervals contain the true mean Î¼ = 1000? If you repeated the simulation, would you expect
exactly the same number of intervals to contain Î¼? In a very large number of samples, what percent of the confidence intervals
would contain Î¼?