1. Suppose your boss wants you to obtain a sample to estimate a population propo

Question

1. Suppose your boss wants you to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the value of the population proportion. You would like to be 99.9% confident that your estimate is within 0.5% (0.005) of the true population proportion. What is the minimum sample size required?

2. A previous study estimated the value of p to be 0.55. Find the minimum sample size required to ensure that your estimate (ˆp)(p^) will be within 0.025 of p with 99% confidence.

3. A previous study gave (0.24, 0.38) as a confidence interval for p. Find the minimum sample size required to ensure that your estimate (ˆp)(p^) will be within 0.09 of p with 99.5% confidence.

Explanation / Answer

Solution

1. Margin of error = +-0.005

Let us assume that p = 0.5

99.9% confidence level, z = +- 3.2905

Margin of error = +-z * ( p * q /(n))0.5

+-0.005 = +-3.2905(0.5*0.5/n)0.5

n = 108,274

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