Suppose a well-designed and executed survey was performed to estimate the proportion of a population in favor of a proposed law. The interval (0.60, 0.70) was calculated as its 95% confidence interval. 2a: What was the estimated proportion of population in favor of the proposed law? How did you calculate that answer? 2b: What was the margin of error of that survey? How did you calculate that answer? 2c: Are you guaranteed to have the true population proportion in that interval of (0.60, 0.70)? Why or why not? 2d: Suppose 20 different survey firms were to execute the same survey on the same population. How many of those surveys should you expect to contain the true population proportion within their 95% confidence interval? Explain your answer and/or show any calculations. 2e: What should you expect to happen to the width of the 95% confidence interval if a new survey were to survey four times as many people as the original survey?
Question 2: Suppose a well-designed and executed survey was performed to estimate the proportion of a population in favor of a proposed law. The interval (0.60, 0.70) was calculated as its 95% confidence interval.
2a: What was the estimated proportion of population in favor of the proposed law? How did you calculate that answer?
2b: What was the margin of error of that survey? How did you calculate that answer?
2c: Are you guaranteed to have the true population proportion in that interval of (0.60, 0.70)? Why or why not?
2d: Suppose 20 different survey firms were to execute the same survey on the same population. How many of those surveys should you expect to contain the true population proportion within their 95% confidence interval? Explain your answer and/or show any calculations.
2e: What should you expect to happen to the width of the 95% confidence interval if a new survey were to survey four times as many people as the original survey?
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