STATISTICAL TECHNIQUES AND TOOLS
CONFIDENCE INTERVALS
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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A random sample has been taken from a population. A statistician, using this sample, needs to decide whether to construct a 90 percent confidence interval for the population mean or a 95 percent confidence interval for the population mean. How will these intervals differ?
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The 90 percent confidence interval will not be as wide as the 95 percent confidence interval.
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The 90 percent confidence interval will be wider than the 95 percent confidence interval.
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Which interval is wider will depend on how large the sample is.
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Which interval is wider will depend on whether the sample is unbiased.
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Which interval is wider will depend on whether a z-statistic or a t-statistic is used.
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Explanation:
Detailed explanation-1: -Answer. Answer: If we had a larger sample size with around the same standard deviation, the 95% confidence interval would be narrower. This is because a larger sample size provides more information and reduces the standard error of the estimate, which leads to a narrower interval.
Detailed explanation-2: -First, calculate the standard error (SE) and the margin of error (ME). SE = /√n. ME = SE × Z(0.90) Then determine the confidence interval range, using ME and -the calculated average (mean). upper bound = + ME. lower bound = -ME. 02-Feb-2023
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