# Sampling Distr. Sample Problem answers - sampling...

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George Mason University School of Management OM 210: STATISTICAL ANALYSIS FOR MANAGEMENT Professor Harvey Singer Sampling Distribution of the Sample Mean Sample Problem Directions: Report all probabilities as decimals to 4 decimal places. Round z to two decimal places to use the standard normal table. A large supermarket chain employs over 9,000 people. It has been stated by the company that the mean age of all of its employees (the population) is 43.7 years with a standard deviation of 8.3 years. The company is thinking of introducing a healthcare package, and its insurance carrier wants to sample 48 employees before quoting a price. Given: μ = 43.7 years σ = 8.3 years n = 48 a. Describe the sampling distribution of the sample mean in terms of (1) the numerical value of its mean, E(xbar) = μ = 43.7 years (2) the numerical value of its standard error of the mean, and σ xbar = σ /√ n = 8.3/√48 = 1.198 years (3) its shape (and you must explain why). Normal, because n = 48 is a large sample (> 30), so by the CLT the

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Unformatted text preview: sampling distribution of xbar is nearly normal. (Or words to this effect, as long as the point is made that this is a large sample, larger than the n = 30 required by the CLT.) © 2008 Harvey A. Singer 1 b. Suppose a single random sample of n = 48 employees was selected. What is the chance that the mean of this sample will be within 2.5 years of the population mean? Want Prob ( μ-2.5 years < xbar < μ +2.5 years) = Prob ( 41.2 years ≤ xbar ≤ 46.2 years) For xbar = 46.2 years, z = (xbar – μ )/ σ xbar = 2.5/1.198 = 2.09 So Prob ( 41.2 years ≤ xbar ≤ 46.2 years) = Prob (-2.09 < z < 2.09) = Prob ( z ≤ 2.09) – Prob (z ≤ -2.09) = 0.9817 +0.0183 = 0.9634 Answer: 0.9634 c. What can the insurance carrier do to reduce the standard error? Focus your answer on issues related only to sampling concepts. To reduce standard error of the mean, increase the sample size: take samples of size greater than 48 employees. © 2008 Harvey A. Singer 2...
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Sampling Distr. Sample Problem answers - sampling...

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