You wish to construct a 95% confidence interval to compare two proportions.If we wish to obtain a margin of error of at most 0.03,what sample size should we take from each group? Assume equal sample sizes.

A) 1067
B) 2134
C) 2135
D) 1068
E) 1984

Question

Angelina Flores · Accepted Answer

Final Answer : C, Explanation :  The formula for calculating the margin of error for a 95% confidence interval for proportions is:Margin of error = z*√((p1*(1-p1))/n1 + (p2*(1-p2))/n2)where z is the z-value for the desired confidence level (1.96 for 95% confidence), p1 and p2 are the estimated proportions for the two groups, and n1 and n2 are the sample sizes for the two groups.Assuming equal sample sizes, we can simplify this formula to:Margin of error = z*√((2*p*(1-p))/n)where p is the pooled proportion (the average of the estimated proportions for the two groups) and n is the sample size for each group.We want the margin of error to be at most 0.03, so we can plug in the values and solve for n:0.03 = 1.96*√((2*(0.5)*(1-0.5))/n)0.03/1.96 = √(0.25/n)Squared both the sides.(0.03/1.96)^2 = 0.25/nn = 0.25/(0.03/1.96)^2n = 2134.68Rounding up to the nearest whole number, we get a sample size of 2135 for each group. Therefore, the best choice is C) 2135.

You wish to construct a 95% confidence interval to compare two proportions.If we wish to obtain a margin of error of at most 0.03,what sample size should we take from each group? Assume equal sample sizes.

A) 1067
B) 2134
C) 2135
D) 1068
E) 1984

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You wish to construct a 95% confidence interval to compare two proportions.If we wish to obtain a margin of error of at most 0.03,what sample size should we take from each group? Assume equal sample sizes.A) 1067B) 2134C) 2135D) 1068E) 1984

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Learning Objectives

Related questions

You wish to construct a 95% confidence interval to compare two proportions.If we wish to obtain a margin of error of at most 0.03,what sample size should we take from each group? Assume equal sample sizes.

A) 1067
B) 2134
C) 2135
D) 1068
E) 1984