Sample Test 3 (estimation) answers

Sample Test 3 (estimation) answers - George Mason...

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George Mason University School of Management OM 210: STATISTICAL ANALYSIS FOR MANAGEMENT Prof. Harvey Singer TEST #3: Inference and Regression (SAMPLE) Confidence Interval Example Problems 1. A process packages refined sugar into small 20-ounce bags. The weights of the contents of these bags (net weight) have a standard deviation of 1.2 ounces. A random sample of 36 bags had mean net weight 19.8 ounces. Let xbar be the random variable of mean weight, in ounces, of a random sample of 20-ounce bags of sugar. (Do not know if the population of weight values of each and every 20-ounce bag produced is normal or not. But the sampling distribution of xbar is approximately normal because the sample size of n = 36 is large enough (36 > 30) for the CLT to apply.) Given: xbar = 19.8 ounces σ = 1.2 ounces n = 36 What do you know in this problem, s or σ ? In this problem, know σ . Use z values in the interval estimation equations. a. What is the point estimate for the mean bag weight? μ ~ 19.8 ounces, from the given xbar b. On the basis of this point estimate, what do you suspect? S uspect that the bags are on average being slightly underfilled. c. Calculate the margin of error at 95% confidence. E = 0.392 ounces d. Calculate the 95% confidence interval based on the sample findings for the true mean weight for all bags of sugar produced by this process. 19.408 ≤ μ ≤ 20.192 ounces e. At 95% confidence, what is the chance that the true mean is actually larger than the upper bound of the 95% confidence interval found in d? 2.5% f. What is the chance that, on average, a bag is actually filled with 20 ounces of sugar? 0.95 © 2010 Harvey A. Singer Page 1 of 3
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g. Based on your results so far, is there a statistical basis for suspecting that the bags being underfilled, on average? NO, the claimed weight of 20 ounces is within the 95% confidence interval h. Find the margin of error between the true and sampled mean net weights at 90% confidence, and compare it to the margin of error of the estimate at 95% confidence. E = 0.329 ounce, slightly smaller than the 95% confidence margin of error i. Calculate the 90% confidence interval based on the sample findings for the true mean weight for all bags of sugar produced by this process. 19.471 ≤ μ ≤ 20.129 ounces j. At 90% confidence, are the bags being underfilled on average? NO, the claimed weight of 20 ounces is within the 90% confidence interval k. Why is the mean weight reported for the sample different from the claimed mean weight? Sampling error, also known as sampling variation l. For the error of the estimate to be no more than 0.25 ounce, how large a sample of randomly chosen bags is required at 95% confidence. n
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Sample Test 3 (estimation) answers - George Mason...

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