Chapter 16 Question 16 (abd) Confidence Intervals, again- Several factors are in

Question

Chapter 16 Question 16 (abd) Confidence Intervals, again- 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? a. For a given sample size, reducing the margin of error will mean lower b. For a certain confidence level, you can get a smaller margin of error by confidence. - selecting a bigger sample. - c. For a fixed margin of error, smaller samples will mean lower confidence.

Explanation / Answer

a)
True
As ME = z * SE, here z is lower for the lower value of CI
Hence this will reduce the ME.

b)
True
As ME = z * SE, here SE = sigma/sqrt(n), higher the value of n will reduce SE and hence decrease ME

c)
True
z = ME/SE, here SE = sigma/sqrt(n), lower the value of n, higher the value of SE and lower value of z i.e. lower CI

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