Essentials of Statistics (5th Edition)

Published by Pearson
ISBN 10: 0-32192-459-2
ISBN 13: 978-0-32192-459-9

Chapter 6 - Normal Probability Distributions - 6-4 Sampling Distributions and Estimators - Page 275: 8

Answer

a. 2.16 b. (4,4); 0 (5,5); 0 (9,9); 0 (4,5); .71 (4,9); 3.536 (5,4); .71 (5,9); 2.828 (9,4); 3.5356 (9,5); 2.828 c) 1.572 d) No

Work Step by Step

a. We know the following equation for standard deviation: $\sigma = \sqrt{\frac{\Sigma(x-\bar{x})^2}{n}}$ $\sigma =2.16$ b. There are 9 possibilities, for there are 3 numbers that can go into 9 different pairs of two. Once again, $\sigma = \sqrt{\frac{\Sigma(x-\bar{x})^2}{n}}$. Each sample has a probability of 1/9. Thus, we find: $Sample; \sigma$ (4,4); 0 (5,5); 0 (9,9); 0 (4,5); .71 (4,9); 3.536 (5,4); .71 (5,9); 2.828 (9,4); 3.5356 (9,5); 2.828 c) Since the probabilities are equal, we can use the normal equation for mean. Thus, the mean is: 1.572. d) Since the results in part a and part c are not the same, we see that the sampling median is not an unbiased predictor.
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