Question

1. You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 95% confident that you estimate is within 3% of the true population proportion. How large of a sample size is required?

2. A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 8% margin of error at a 90% confidence level, what size of sample is needed

3. You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=45.1σ=45.1. You would like to be 98% confident that your estimate is within 4 of the true population mean. How large of a sample size is required?

4. You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately σ=51.3σ=51.3 dollars. You would like to be 95% confident that your estimate is within 1.5 dollar(s) of average spending on the birthday parties. How many parents do you have to sample?

Answer 1

1. Let, population proportion, p = 0.5

Margin of error, E = 3% = 0.03

Confidence Level, CL = 0.95

Significance level, α = 1 - CL = 0.05

Critical value, z = NORM.S.INV(0.05/2) = 1.96

Sample size, n = (z² * p * (1-p)) / E² = (1.96² * 0.5 * 0.5)/ 0.03²

= 1067.0719 = 1067

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2. Let, population proportion, p = 0.5

Margin of error, E = 0.08

Confidence Level, CL = 0.9

Significance level, α = 1 - CL = 0.1

Critical value, z = NORM.S.INV(0.1/2) = 1.6449

Sample size, n = (z² * p * (1-p)) / E² = (1.6449² * 0.5 * 0.5)/ 0.08²

= 105.6853 = 106

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3. Population standard deviation, σ = 45.1

Margin of error, E = 4

Confidence interval, CL = 0.98

Significance level, α = 1-CL = 0.02

Critical value, z = NORM.S.INV(0.02/2) = 2.3263

Sample size, n = (z * σ / E)² = (2.3263 * 45.1 / 4)² = 687.99 = 688

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4. Population standard deviation, σ = 51.3

Margin of error, E = 1.5

Confidence interval, CL = 0.95

Significance level, α = 1-CL = 0.05

Critical value, z = NORM.S.INV(0.05/2) = 1.96

Sample size, n = (z * σ / E)² = (1.96 * 51.3 / 1.5)² = 4493.12 = 4493