question archive Several factors are involved in the creation of a confidence interval
Several factors are involved in the creation of a confidence interval
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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, higher confidence means a smaller margin of error.
This statement is _____
b) For a specified confidence level, larger samples provide smaller margins of error.
This statement is _____
c) For a fixed margin of error, larger samples provide greater confidence.
This statement is _____
d) For a given confidence level, halving the margin of errors requires a sample size twice as large.
This statement is _____
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Answer:
a) False.
For a given sample size higher confidence means a larger margin of error.
b) True.
Larger samples lead to smaller standard errors (SE) which lead to a smaller margin of error.
c) True.
Larger samples are less variable, which makes us more confident that a given interval succeeds in catching the true population proportion.
d) False.
The margin of error (ME) decreases as the square root of the sample size increases. Halving the margin of error requires a sample four times as large as the original
