You wish to construct a 90% confidence interval to compare two proportions.If we wish to obtain a margin of error of at most 0.05,what sample size should we take from each group? Assume equal sample sizes.

A) 1984
B) 271
C) 270
D) 542
E) 541

Question

Katharina Martinez · Accepted Answer

Final Answer : D, Explanation :  To find the sample size required for each group, we can use the following formula:n = [(Zα/2)^2 * (p̂ * q̂)/(E)^2]/2where- Zα/2 is the z-score corresponding to the level of confidence (90% in this case),- p̂ and q̂ are the sample proportions,- E is the maximum margin of error we want.Since we are comparing two proportions, we can assume both have the same sample size, denoted by n.If we take the worst-case scenario where p̂ = q̂ = 0.5 (which maximizes the sample size), we get:n = [(Zα/2)^2 * (0.5 * 0.5)/(E)^2]/2n = [(1.645)^2 * (0.25)/(0.05)^2]/2n ≈ 270.51Rounding up to the nearest integer, we get a sample size of n = 271. Therefore, the options that satisfy the condition of having a sample size of at least 271 are D) 542 and E) 541 (assuming we have equal sample sizes in each group).

You wish to construct a 90% confidence interval to compare two proportions.If we wish to obtain a margin of error of at most 0.05,what sample size should we take from each group? Assume equal sample sizes.

A) 1984
B) 271
C) 270
D) 542
E) 541

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Learning Objectives

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You wish to construct a 90% confidence interval to compare two proportions.If we wish to obtain a margin of error of at most 0.05,what sample size should we take from each group? Assume equal sample sizes.A) 1984B) 271C) 270D) 542E) 541

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Learning Objectives

Learning Objectives

Related questions

You wish to construct a 90% confidence interval to compare two proportions.If we wish to obtain a margin of error of at most 0.05,what sample size should we take from each group? Assume equal sample sizes.

A) 1984
B) 271
C) 270
D) 542
E) 541