Confidence Intervals: Calculations and Applications in Statistical Inference

Explores confidence interval calculations in statistics.

Amelia Davis

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Confidence Intervals: Calculations and Applicationsin Statistical InferenceWhy is a 99% confidence interval wider than a 95%confidence interval?Solution)The definition of a confidence interval is that it contains the true populationmean. If Ihave a 95% confidence interval, that means I am 95% certainthat the true population mean is in the interval. If I want to be even morecertain, I have to widen the interval. If I can be less certain, I can narrowthe interval.So the widestinterval will be 99%, and the narrowest would be 90%.Example:you're trying to figure out where in the city Comet Donuts is in, but youreally don't know for sure. A desperately hungry person hands you a mapand asks you to show him where it is. If someone forces you to be 99%accurate, are you going to draw a wide or narrow circle on the map? Youcan't afford to be wrong-at 99% you're saying that you'll be wrong onetime out of 100! So you draw a big circle.If the person asking doesn't even like donuts, they're just asking for theheck of it, you can be 90% accurate, so you can take a chance and draw asmall circle. You'll be wrong 10% of the time.12.A person claims to be able to predict the outcome offlipping a coin. This person is correct16/25 times. Computethe 95% confidence interval on the proportion of times thisperson can predict coin flips correctly. What conclusion canyou draw about this test of his ability to predict the future?Solution)WE HAVE GIVEN THAT n = 25 and p = 16/25And we need to construct the 95% C.I. for the proportion of times thisperson can predict coins flips correctly as,ṕ± 1.96 *√(ṕq^/n)=.64± 1.96 *√(.64*.36/25)= .64 ± .1882

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Confidence Intervals: Calculations and Applications in Statistical Inference

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