Several factors are involved in the creation of a confidence interval. Among the

Question

Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true? Select all true statements below. A. For a certain confidence level, you can get a smaller margin of error by selecting a bigger sample. B. For a given confidence level, a sample 9 times as large will make a margin of error one third as big. C. For a fixed margin of error, smaller samples will mean lower confidence. D. For a given sample size, reducing the margin of error will mean lower confidence. E. None of these statements are true.

Explanation / Answer

Confidence interval = Xbar +/- Z*Sigma/Sqrt(n)

n=sample size, Z =Z value, Sigma = stdev, Xbar = average value of sample of X

The 2nd part of CI is margin of error.

Hence, A is true

B is True. The margin of error depends as 1/sqrt(n). So, 1/sqrt(9) = 1/3 as much

C is not true. Fixing margin of error will fix CI

D is true. Z will have to decrease then. which means decrease in confidence

E is false.

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