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A RANDOM SAMPLE OF 10 ECONOMISTS PRODUCED THE FOLLOWING

A RANDOM SAMPLE OF 10 ECONOMISTS PRODUCED THE FOLLOWING

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Author: Christine Farr
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 A random sample of 10 economists produced the following forecasts for percentagegrowth in real domestic product in the next year: 2.2 2.8 3.0 2.5 2.4 2.6 2.5 2.4 2.7 2.6Use unbiased estimation procedures to find point estimates for the following:a. The population mean?b. The population variance?c. The variance of the sample meand. The population proportion of economists predicting growth of at least 2.5% in realgross domestic producte. The variance of the sample proportion of economists predicting growth of at least2.5% in real gross domestic product2. A college admissions officer for an MBA program has determined that historicallyapplicants have undergraduate grade point averages that are normally distributed withstandard deviation 0.45. From a random sample of 25 applications from the current year,the sample mean grade point average is 2.90.a. Find a 95% confidence interval for the population mean?b. Without doing calculations, explain whether a 99% confidence interval for thepopulation mean would be wider than, narrower than, or the same width as found in parta.c. Suppose that population standard deviation is 0.56 (instead of 0.45), without doingcalculations explain whether a 95% confidence interval for the population mean would bewider than, narrower than, or the same width as found in part (a).d. Suppose that sample mean that is given in the problem is calculated from a sample ofsize 40 (instead of 25), without doing calculations explain whether a 95% confidenceinterval for the population mean would be wider than, narrower than, or the same widthas found in part (a).e. Based on these sample results, a statistician computes for the population mean aconfidence interval extending from 2.81 to 2.99. Find the confidence level associatedwith this interval.f. Suppose that we know that grade point averages that are normally distributed, but we 

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