329 APPLET Confidence Intervals for a Proportion 6.3 ACTIVITY You can find the interactive applet for this activity at MyLab Statistics. SECTION 6.3 Confidence Intervals for Population Proportions 329 The Confidence intervals for a proportion applet allows you to visually investigate confidence intervals for a population proportion. You can specify the Sample size and the population proportion p. When you click Update applet, 100 separate samples of the specified size are selected from a population with a proportion of successes equal to p. For each of the 100 samples, a 95% confidence interval is displayed in green when it includes the mean, or in red when it does not include the mean. Each time you click Update applet you get a new simulation. The level of confidence used for the intervals can be changed within the applet itself by updating the CI level input. You can generate additional samples with the given confidence interval by clicking 100 intervals or 1000 intervals. Each of these intervals is computed using the standard normal approximation. The cumulative number of times intervals that contain the population proportion is also shown. Press Reset to clear existing results and start a new simulation. EXPLORE Step 1 Specify a Sample size. Step 2 Specify a value for p. Step 3 Click Update applet, 100 intervals, or 1000 intervals to generate confidence intervals. DRAW CONCLUSIONS 1. At the 95% confidence level, generate 1000 confidence intervals with p = 0.6 for each Sample size: 10, 20, 40, and 100. Clear your results after each simulation. What proportion of the confidence intervals for each sample size contains the population proportion? What happens as the sample size increases? 2. Generate 1000 confidence intervals for p = 0.6 and Sample size = 100 at each of several different confidence levels. Describe how the proportion of confidence intervals that contain the population proportion changes as the confidence level increases. Explain your result. APPLET Confidence intervals for p, p=0.5 Type=Standard-Wald 100 intervals Sample size 1000 intervals Update Applet Reset Info Sort graph Sample size: p: 50 50 0.5 Intervals 1 to 100 0 0.2 0.8 0.6 0.4 Intervals CI Level 0.80 82 100 79 Containing p Total Prop. contain 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
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