Question

1. Access the Explore Coverage web app. Select "Confidence Interval for a Proportion", set p 0.5, n=50 and Confidence Level to 95. Select 10 samples. i) Click the Draw Samples button. Describe what appears: 1. What do the green/red squares represent? 2. What do the lines extending from the squares represent? ii) Click the Draw Samples button again until a red square (and lines) appears. What is the significance of a red square and lines? i) Continue generating samples until you have generated 100 Report the proportion of intervals that correctly capture the true population mean. Insert an image of the Coverage Plot below iv) Repeat (iii) for samples of size 100. How are the intervals different from those in (ii)? Report the proportion of intervals that correctly capture true population mean. Insert an image of the Coverage Plot below. Should increasing the sample size result in a Coverage Percent closer to 95% iv) Repeat (ii) for samples of size 100. How are the intervals different from those in (ii)? Report the proportion of intervals that correctly capture true population mean. Insert an image of the Coverage Plot below. Should increasing the sample size result in a Coverage Percent closer to 95% v) Repeat (iii) for a confidence level of 90% (and samples of size of 50). Report the proportion of intervals that correctly capture true population mean. Paste an image of the Coverage Plot below

Answer 1

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Coverage of Confidence Interval Nominal confidence level: 95%, n = 50, p = 0.5 After 100 simulations: 95 intervals cover, 5 don't 5.0% do not cov #95.0% cover overage: 0.0 0.1 02 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Population Proportion p

Nominal confidence level: 95%, n = 50, p After 1000 simulations: 931 intervals cover, 69 don't 0.5 overage: 93.1% Cover 6.9% do not cov 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Population Proportion p

Coverage of Confidence Interval Nominal confidence level: 90%, n 50, p = 0.5 After 5000 simulations: 4406 intervals cover, 594 don't 88.1% Cover overage: 11.9% do not co CS 0.0 0.1 0.20.3 0.4 0.5 0.6 0.7 0,8 0.9 1.0
this time coverage is 88 percentage