Applet Exercise What happens if we attempt to use the applet ConfidenceIntervalP

Chapter 8, Problem 8.51

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Applet Exercise What happens if we attempt to use the applet ConfidenceIntervalP (accessible at www.thomsonedu.com/statistics/wackerly) to reproduce the results presented in Figure 8.8? Access the applet. Dont change the value of p from .50 or the confidence coeffi- cient from .95, but use the Sample Size button to change the sample size to n = 35. Click the button One Sample a single time. In the top left portion of the display, the sample values are depicted by a set of 35 0s and 1s, and the value of the estimate for p and the resulting 95% confidence interval are given below the sample values. a What is the value of p that you obtained? Is it the same as the first value obtained, 0.5143, when Figure 8.8 was generated? Does this surprise you? Why? b Use the value of the estimate that you obtained and the formula for a 95% confidence interval to verify that the confidence interval given on the display is correctly calculated. c Does the interval that you obtained contain the true value of p? d What is the length of the confidence interval that you obtained? Is it exactly the same as the length of first interval, (.3487, .6799), obtained when Figure 8.8 was generated? Why? e Click the button One Sample again. Is this interval different than the one previously generated? Click the button One Sample three more times. How many distinctly different intervals appear among the first 5 intervals generated? How many of the intervals contain .5? f Click the button One Sample until you have obtained 24 intervals. What percentage of the intervals contain the true value of p = .5? Is the percentage close to the value that you expected?