Explanation Calculation: Step-by-step procedure to generate 200 random samples using the MINITAB software: Click on Calc > Random Data > Binomial Distribution . In Number of rows of data to generate section, enter 200 . In the Store in column , enter column C1 named as Random Numbers . For Number of trails , enter 20 . For Probability , enter 0.6 . Click OK .. Output using the MINITAB is given below: Random numbers 9 15 12 16 12 9 15 11 12 10 10 9 14 16 11 11 9 15 13 12 11 6 15 11 15 9 11 11 14 11 9 13 9 12 13 12 13 15 12 13 11 9 10 12 9 12 14 10 15 12 10 8 11 12 10 15 13 10 11 10 14 8 12 14 13 12 10 12 13 7 15 13 11 8 17 11 10 10 15 12 9 15 11 10 13 12 11 10 10 17 12 15 12 12 18 15 9 11 14 9 10 15 13 14 12 9 14 17 15 6 9 13 13 14 13 17 15 15 13 13 15 11 10 9 9 8 14 12 12 13 9 12 10 8 14 13 12 7 15 13 8 9 15 14 11 9 11 14 11 11 14 9 11 15 10 11 14 14 14 11 9 10 11 17 12 13 15 10 12 8 8 13 14 15 9 16 11 15 10 7 11 13 16 11 8 14 9 12 10 12 12 13 11 15 12 12 12 16 12 12 From the Standard Normal Table, the z value for 90% level is 1.645. The general formula for the confidence interval for the binomial parameter is, p ^ ± z 1 − α 2 p ^ q ^ n The lower bound and upper bound is tabulated below: Random Numbers p ^ q ^ = 1 − p ^ z 1 − α 2 S E = z 1 − α 2 p ^ q ^ n Lower bound Upper bound 9 0.45 0.55 1.645 0.1830 0.2670 0.6330 10 0.5 0.5 1.645 0.1839 0.3161 0.6839 11 0.55 0.45 1.645 0.1830 0.3670 0.7330 9 0.45 0.55 1.645 0.1830 0.2670 0.6330 11 0.55 0.45 1.645 0.1830 0.3670 0.7330 10 0.5 0.5 1.645 0.1839 0.3161 0.6839 14 0.7 0.3 1.645 0.1686 0.5314 0.8686 15 0.75 0.25 1.645 0.1593 0.5907 0.9093 9 0.45 0.55 1.645 0.1830 0.2670 0.6330 12 0.6 0.4 1.645 0.1802 0.4198 0.7802 10 0.5 0.5 1.645 0.1839 0.3161 0.6839 9 0.45 0.55 1.645 0.1830 0.2670 0.6330 15 0.75 0.25 1.645 0.1593 0.5907 0.9093 9 0.45 0.55 1.645 0.1830 0.2670 0.6330 8 0.4 0.6 1.645 0.1802 0.2198 0.5802 14 0.7 0.3 1.645 0.1686 0.5314 0.8686 9 0.45 0.55 1.645 0.1830 0.2670 0.6330 8 0.4 0.6 1.645 0.1802 0.2198 0.5802 11 0.55 0.45 1.645 0.1830 0.3670 0.7330 12 0.6 0.4 1.645 0.1802 0.4198 0.7802 15 0.75 0.25 1.645 0.1593 0.5907 0.9093 9 0.45 0.55 1.645 0.1830 0.2670 0.6330 6 0.3 0.7 1.645 0.1686 0.1314 0.4686 13 0.65 0.35 1.645 0.1754 0.4746 0.8254 9 0.45 0.55 1.645 0.1830 0.2670 0.6330 8 0.4 0.6 1.645 0.1802 0.2198 0.5802 8 0.4 0.6 1.645 0.1802 0.2198 0.5802 13 0.65 0.35 1.645 0.1754 0.4746 0.8254 15 0.75 0.25 1.645 0.1593 0.5907 0.9093 15 0.75 0.25 1.645 0.1593 0.5907 0.9093 15 0.75 0.25 1.645 0.1593 0.5907 0.9093 13 0.65 0.35 1.645 0.1754 0.4746 0.8254 11 0.55 0.45 1.645 0.1830 0.3670 0.7330 12 0.6 0.4 1.645 0.1802 0.4198 0.7802 9 0.45 0.55 1.645 0.1830 0.2670 0.6330 9 0.45 0.55 1.645 0.1830 0.2670 0.6330 10 0.5 0.5 1.645 0.1839 0.3161 0.6839 13 0.65 0.35 1.645 0.1754 0.4746 0.8254 13 0.65 0.35 1.645 0.1754 0.4746 0.8254 13 0.65 0.35 1.645 0.1754 0.4746 0.8254 12 0.6 0.4 1.645 0.1802 0.4198 0.7802 14 0.7 0.3 1.645 0.1686 0.5314 0.8686 15 0.75 0.25 1.645 0.1593 0.5907 0.9093 9 0.45 0.55 1.645 0.1830 0.2670 0.6330 10 0.5 0.5 1.645 0.1839 0.3161 0.6839 11 0.55 0.45 1.645 0.1830 0.3670 0.7330 12 0.6 0.4 1.645 0.1802 0.4198 0.7802 11 0.55 0.45 1.645 0.1830 0.3670 0.7330 11 0.55 0.45 1.645 0.1830 0.3670 0.7330 12 0.6 0.4 1.645 0.1802 0.4198 0.7802 13 0.65 0.35 1.645 0.1754 0.4746 0.8254 13 0.65 0.35 1.645 0.1754 0.4746 0.8254 10 0.5 0.5 1.645 0.1839 0.3161 0.6839 10 0.5 0.5 1.645 0.1839 0.3161 0.6839 15 0.75 0.25 1.645 0.1593 0.5907 0.9093 11 0.55 0.45 1.645 0.1830 0.3670 0.7330 11 0.55 0.45 1.645 0.1830 0.3670 0.7330 14 0.7 0.3 1.645 0.1686 0.5314 0.8686 16 0.8 0.2 1.645 0.1471 0.6529 0.9471 11 0.55 0.45 1.645 0.1830 0.3670 0.7330 16 0.8 0.2 1.645 0.1471 0.6529 0.9471 16 0.8 0.2 1.645 0.1471 0.6529 0.9471 11 0.55 0.45 1.645 0.1830 0.3670 0.7330 12 0.6 0.4 1.645 0.1802 0.4198 0.7802 12 0.6 0.4 1.645 0.1802 0.4198 0.7802 12 0.6 0.4 1.645 0.1802 0.4198 0.7802 14 0.7 0.3 1.645 0.1686 0.5314 0.8686 8 0.4 0.6 1.645 0.1802 0.2198 0.5802 10 0.5 0.5 1.645 0.1839 0.3161 0.6839 12 0.6 0.4 1.645 0.1802 0.4198 0.7802 14 0.7 0.3 1.645 0.1686 0.5314 0.8686 14 0.7 0.3 1.645 0.1686 0.5314 0.8686 9 0.45 0.55 1.645 0.1830 0.2670 0.6330 8 0.4 0.6 1.645 0.1802 0.2198 0.5802 14 0.7 0.3 1.645 0.1686 0.5314 0.8686 15 0.75 0.25 1.645 0.1593 0.5907 0.9093 17 0.85 0.15 1.645 0.1313 0.7187 0.9813 15 0.75 0.25 1.645 0.1593 0.5907 0.9093 11 0.55 0.45 1.645 0.1830 0.3670 0.7330 15 0.75 0.25 1.645 0.1593 0.5907 0.9093 12 0.6 0.4 1.645 0.1802 0.4198 0.7802 11 0

8th Edition

ISBN: 9781305268920

Author: Bernard Rosner

Publisher: Cengage Learning

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Chapter 6, Problem 93P

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Check whether the large-sample binomial confidence limit formula is adequate for the given distribution.

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Chapter 6, Problem 92P

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