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Confidence Intervals and Statistical Inference: Homework Assignments and Solutions Week 5

Practice problems on confidence intervals and statistical inference techniques.

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Confidence Intervals and Statistical Inference: Homework Assignments andSolutionsHamiltonWeek 5 Homework4.Why is a 99% confidence interval wider than a 95% confidence interval?Solution)The definition of a confidence interval is that itcontains 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%.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 theproportion 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)=.64± 1.96 *√(.64*.36/25)= .64 ± .1882So the 95% C.I. is,(0.4518,0.8282)So We Are 95 OutOf 100Attemptsare confident thatthe values of the samples are lies b/w(.4518,.8282)15.You take a sample of 22 from a population of test scores, and the mean of your sample is60.(a) You know the standard deviation of the population is 10. What is the 99% confidenceinterval on the populationmean?Solution)

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