Confidence intervals in action. The idea of an 80% confidence interval is thatthe

Chapter 0, Problem 14.3

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Confidence intervals in action. The idea of an 80% confidence interval is thatthe interval captures the true parameter value in 80% of all samples. Thats nothigh enough confidence for practical use, but 80% hits and 20% misses make iteasy to see how a confidence interval behaves in repeated samples from the samepopulation. Go to the Confidence Interval applet.(a) Set the confidence level to 80%. Click Sample to choose an SRS andcalculate the confidence interval. Do this 10 times to simulate 10 SRSs with their 10 confidence intervals. How many of the 10 intervals captured the true mean ?How many missed?(b) You see that we cant predict whether the next sample will hit or miss. Theconfidence level, however, tells us what percent will hit in the long run. Reset theapplet and click Sample 50 to get the confidence intervals from 50 SRSs. Howmany hit? Keep clicking Sample 50 and record the percent of hits among 100,200, 300, 400, 500, 600, 700, 800, and 1000 SRSs. Even 1000 samples is not trulythe long run, but we expect the percent of hits in 1000 samples to be fairly closeto the confidence level, 80%.