(Solution) - A study is planned to estimate the proportion of businesses -(2025 Original AI-Free Solution)

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A study is planned to estimate the proportion of businesses started in the year 2006 that had failed within five years of their start-up. How large a sample size is needed to guarantee estimating this proportion correct to within
a. 0.10 with probability 0.95?
b. 0.05 with probability 0.95?
c. 0.05 with probability 0.99?
d. Compare sample sizes for parts a and b, and b and c, and summarize the effects of decreasing the margin of error and increasing the confidence level.