After deciding on a 95% confidence level, a researcher is trying to decide what sample size to use. Using a sample size of 800 instead of 200 would increase the cost to conduct her research, but how will it affect her margin of error?
Answer
A
The interval will be more likely to capture the true population parameter because it will be wider.
B
The interval will be less likely to capture the true population parameter because it will be narrower.
C
The margin of error will be cut in half.
D
The margin of error will be doubled.
Explanation
For a fixed 95% confidence level, the margin of error is proportional to 1/√n, where n is the sample size. Increasing the sample from 200 to 800 multiplies it by 4, so the margin of error is multiplied by 1/√4 = 1/2. Thus, the margin of error will be cut in half.
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