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Statistical Analysis and Confidence Intervals: A Comprehensive Approach to Estimating Population Parameters

Covers statistical methods for estimating population parameters.

Amelia Ward
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Statistical Analysis and Confidence Intervals: A Comprehensive Approach toEstimating Population ParametersWhy is a 99% confidence interval wider than a 95% confidence interval?Solution)The definition of a confidence interval is that it contains the true population mean. If I have a95% confidence interval, that means I am 95% certain that the true population mean is in theinterval. If I want to be even more certain, I have to widen the interval. If I can be less certain, Ican narrow the interval.So the widest interval 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 you really don't know forsure. A desperately hungry person hands you a map and asks you to show him where it is. Ifsomeone forces you to be 99% accurate, are you going to draw a wide or narrow circle on themap? You can't afford to be wrong-at 99% you're saying that you'll be wrong one time out of100! So you draw a big circle.If the person asking doesn't even like donuts, they're just asking for the heck of it, you can be90% accurate, so you can take a chance and draw a small circle. You'll be wrong 10% of thetime.12.A person claims to be able to predict the outcome of flipping a coin. This person is correct16/25 times. Compute the 95% confidence interval on the proportion of times this person canpredict coin flips correctly. What conclusion can you draw about this test of his ability topredict the future?Solution)WE HAVE GIVEN THAT n = 25 and p= 16/25And we need to constructthe 95% C.I. for the proportion of times this person can predict coinsflips correctly as,ṕ± 1.96 *√(ṕq^/n)

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