You wish to construct a 95% confidence interval to compare the mean measurement for two groups.A small pilot study yields sample standard deviations of 20 and 30 for Group 1 and Group 2,respectively.If we wish to obtain a margin of error of at most 10,what sample size should we take from each group? Assume equal sample sizes.
A)49
B)47
C)50
D)48
E)51

Question

Quizplus · Accepted Answer

To calculate the sample size required for each group, we need to use the following formula:

n = [(zα/2 * σ) / E]^2

Where,

zα/2 = the z-score corresponding to the desired confidence level (95% corresponds to z=1.96)
σ = the sample standard deviation
E = the desired margin of error

Plugging in the given values,

n = [(1.96 * 30) / 10]^2
n = 49.536

We need to round this up to the nearest integer since we cannot have a fractional number of samples, so we get:

n = 50

Hence, we need to take a sample size of 50 from each group to obtain a 95% confidence interval with a margin of error of at most 10. Therefore, the answer is C) 50.

You Wish to Construct a 95% Confidence Interval to Compare