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A 95% confidence interval was constructed for a population mean (sigma known). Suppose we are planning to repeat the study but we only have sufficient resources to take a sample that is one quarter the size of that used in the original study. Assuming we require the same level of confidence (and sigma has not changed), then the resulting margin of error (m.o.e.) for our new confidence interval will be:Group of answer choices √ 2 times the original margin of error 4 times the original margin of errortwice the original margin of error 1/4 times the original margin of error 1/√ 2 times the original margin of error

Question

A 95% confidence interval was constructed for a population mean (sigma known). Suppose we are planning to repeat the study but we only have sufficient resources to take a sample that is one quarter the size of that used in the original study. Assuming we require the same level of confidence (and sigma has not changed), then the resulting margin of error (m.o.e.) for our new confidence interval will be:Group of answer choices √ 2 times the original margin of error 4 times the original margin of errortwice the original margin of error 1/4 times the original margin of error 1/√ 2 times the original margin of error

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Solution

The correct answer is: "2 times the original margin of error"

Here's why:

The margin of error in a confidence interval is given by the formula: Z * (σ/√n), where Z is the Z-score (which depends on the desired level of confidence), σ is the population standard deviation, and n is the sample size.

If the sample size is reduced to one quarter of its original size, then the new margin of error will be: Z * (σ/√(n/4)) = Z * (σ/(√n/2)) = 2 * Z * (σ/√n).

Therefore, the new margin of error will be twice the original margin of error.

This problem has been solved

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