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 50 . For Probability , enter 0.6 . Click OK . Click on Stat > Tables > Tally Individual Variables . In Variables select the column of Random integers In Display select Counts and Percent. Click OK . Output using the MINITAB is given below: Random Numbers 32 32 22 32 27 26 30 29 31 33 27 26 33 32 32 24 28 35 26 29 29 34 30 33 32 33 32 29 32 26 36 27 23 35 32 27 31 31 28 31 32 32 32 33 29 26 26 34 28 26 21 33 29 27 28 35 33 29 28 29 31 31 31 31 30 35 33 28 31 31 33 26 29 31 28 36 33 35 28 26 34 28 28 35 30 34 36 30 35 29 31 30 33 29 28 38 27 30 37 26 30 30 34 38 31 30 27 28 26 31 26 29 36 26 27 34 31 35 23 31 32 29 31 32 31 29 29 28 23 30 33 27 36 22 28 23 23 30 22 23 35 28 34 24 30 28 31 27 29 31 32 24 28 28 27 31 36 32 23 31 29 33 35 30 25 31 29 28 34 31 25 25 29 28 38 24 27 30 37 27 23 33 29 30 28 28 28 29 31 37 30 33 31 29 27 32 28 31 31 31 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 32 0.64 0.36 1.645 0.11167 0.52833 0.75167 33 0.66 0.34 1.645 0.11020 0.54980 0.77020 26 0.52 0.48 1.645 0.11623 0.40377 0.63623 29 0.58 0.42 1.645 0.11482 0.46518 0.69482 31 0.62 0.38 1.645 0.11292 0.50708 0.73292 26 0.52 0.48 1.645 0.11623 0.40377 0.63623 28 0.56 0.44 1.645 0.11548 0.44452 0.67548 31 0.62 0.38 1.645 0.11292 0.50708 0.73292 29 0.58 0.42 1.645 0.11482 0.46518 0.69482 34 0.68 0.32 1.645 0.10852 0.57148 0.78852 35 0.7 0.3 1.645 0.10661 0.59339 0.80661 27 0.54 0.46 1.645 0.11595 0.42405 0.65595 31 0.62 0.38 1.645 0.11292 0.50708 0.73292 36 0.72 0.28 1.645 0.10445 0.61555 0.82445 32 0.64 0.36 1.645 0.11167 0.52833 0.75167 23 0.46 0.54 1.645 0.11595 0.34405 0.57595 23 0.46 0.54 1.645 0.11595 0.34405 0.57595 30 0.6 0.4 1.645 0.11397 0.48603 0.71397 28 0.56 0.44 1.645 0.11548 0.44452 0.67548 29 0.58 0.42 1.645 0.11482 0.46518 0.69482 34 0.68 0.32 1.645 0.10852 0.57148 0.78852 27 0.54 0.46 1.645 0.11595 0.42405 0.65595 28 0.56 0.44 1.645 0.11548 0.44452 0.67548 31 0.62 0.38 1.645 0.11292 0.50708 0.73292 32 0.64 0.36 1.645 0.11167 0.52833 0.75167 27 0.54 0.46 1.645 0.11595 0.42405 0.65595 29 0.58 0.42 1.645 0.11482 0.46518 0.69482 32 0.64 0.36 1.645 0.11167 0.52833 0.75167 31 0.62 0.38 1.645 0.11292 0.50708 0.73292 26 0.52 0.48 1.645 0.11623 0.40377 0.63623 35 0.7 0.3 1.645 0.10661 0.59339 0.80661 30 0.6 0.4 1.645 0.11397 0.48603 0.71397 31 0.62 0.38 1.645 0.11292 0.50708 0.73292 28 0.56 0.44 1.645 0.11548 0.44452 0.67548 29 0.58 0.42 1.645 0.11482 0.46518 0.69482 30 0.6 0.4 1.645 0.11397 0.48603 0.71397 30 0.6 0.4 1.645 0.11397 0.48603 0.71397 26 0.52 0.48 1.645 0.11623 0.40377 0.63623 29 0.58 0.42 1.645 0.11482 0.46518 0.69482 30 0.6 0.4 1.645 0.11397 0.48603 0.71397 30 0.6 0.4 1.645 0.11397 0.48603 0.71397 28 0.56 0.44 1.645 0.11548 0.44452 0.67548 28 0.56 0.44 1.645 0.11548 0.44452 0.67548 33 0.66 0.34 1.645 0.11020 0.54980 0.77020 31 0.62 0.38 1.645 0.11292 0.50708 0.73292 30 0.6 0.4 1.645 0.11397 0.48603 0.71397 28 0.56 0.44 1.645 0.11548 0.44452 0.67548 29 0.58 0.42 1.645 0.11482 0.46518 0.69482 22 0.44 0.56 1.645 0.11548 0.32452 0.55548 26 0.52 0.48 1.645 0.11623 0.40377 0.63623 29 0.58 0.42 1.645 0.11482 0.46518 0.69482 26 0.52 0.48 1.645 0.11623 0.40377 0.63623 28 0.56 0.44 1.645 0.11548 0.44452 0.67548 34 0.68 0.32 1.645 0.10852 0.57148 0.78852 33 0.66 0.34 1.645 0.11020 0.54980 0.77020 35 0.7 0.3 1.645 0.10661 0.59339 0.80661 28 0.56 0.44 1.645 0.11548 0.44452 0.67548 28 0.56 0.44 1.645 0.11548 0.44452 0.67548 31 0.62 0.38 1.645 0.11292 0.50708 0.73292 37 0.74 0.26 1.645 0.10204 0.63796 0.84204 27 0.54 0.46 1.645 0.11595 0.42405 0.65595 27 0.54 0.46 1.645 0.11595 0.42405 0.65595 31 0.62 0.38 1.645 0.11292 0.50708 0.73292 33 0.66 0.34 1.645 0.11020 0.54980 0.77020 22 0.44 0.56 1.645 0.11548 0.32452 0.55548 31 0.62 0.38 1.645 0.11292 0.50708 0.73292 27 0.54 0.46 1.645 0.11595 0.42405 0.65595 35 0.7 0.3 1.645 0.10661 0.59339 0.80661 25 0.5 0.5 1.645 0.11632 0.38368 0.61632 37 0.74 0.26 1.645 0.10204 0.63796 0.84204 28 0.56 0.44 1.645 0.11548 0.44452 0.67548 27 0.54 0.46 1.645 0.11595 0.42405 0.65595 32 0.64 0.36 1.645 0.11167 0.52833 0.75167 33 0.66 0.34 1.645 0.11020 0.54980 0.77020 34 0.68 0.32 1.645 0.10852 0.57148 0.78852 36 0.72 0.28 1.645 0.10445 0.61555 0.82445 31 0.62 0.38 1.645 0.11292 0.50708 0.73292 28 0.56 0.44 1.645 0.11548 0.44452 0.67548 29 0.58 0.42 1.645 0.11482 0.46518 0.69482 33 0.66 0.34 1.645 0.11020 0.54980 0.77020 36 0.72 0.28 1.645 0.10445 0.61555 0.82445 35 0.7 0.3 1.645 0.10661 0.59339 0.80661 30 0.6 0.4 1.645 0.11397 0.48603 0.71397 26 0.52 0.48 1.645 0.11623 0

8th Edition

ISBN: 9781305268920

Author: Bernard Rosner

Publisher: Cengage Learning

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Chapter 6, Problem 96P

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Check whether the large-sample binomial confidence limit formula is adequate for a binomial distribution with n=50and p=0.6.

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Chapter 6, Problem 95P

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Example 4 (Part 2) We can use Statkey to take 50 different random samples of size 20 each, find the mean of each sample, and compute a confidence interval for each one. The graph of the sampling distribution of the means is on the left below, and that of the 50 confidence intervals is on the right. 1. What does each dot on the left hand dotplot represent? StatKey Sampling Distribution for a Mean Percent with Internet Access (Countries) ▾ Show Data Table Edit Data Choose samples of size n = 20 Upload File Change Column(s) Generate 1 Sample Generate 10 Samples Generate 100 Samples Generate 1000 Samples Reset Plot Sampling Dotplot of Mean Left Tail Two-Tail Right Tail 60 50 40 40 30 20 20 10 samples = 50 mean = 41.626 std. error = 5.089 : .: : :: 0 25 30 35 40 45 50 55 60 41.626 Data Plots Confidence Intervals 95%-> Confidence Intervals Coverage 48/50 = 96% 20 40 60 80 2. Circle the confidence intervals that failed to capture the true mean. 3. Circle the sample means that produced those…

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