A confidence interval is a really useful statistical tool. Since most population

Question

A confidence interval is a really useful statistical tool. Since most populations are so big, we can never actually determine what the mean and standard deviation of the population is. So, we take that data from a sample and, using a confidence interval, we create a range in which we would expect to find the population parameters. In other words, we use the confidence intervals to estimate the mean. After reading this section of the text, can you paraphrase and describe the confidence interval? What happens if the interval gets smaller? What happens if the interval gets wider? Can we control that and if so, how?

Explanation / Answer

confidence interval is a set of value where we expect our parameter to lie with certain level of confidence ,

Usually we take it as 95 %

When interval gets smaller ,then we can find parameter in small interval , which is more precise.

if the interval gets wider, it is less precise.

We can control confidence interval ,

by sample size ,

as sample size increases, interval decreases .

for example confidence of interval of proportion is

(p^ - z/2 * sqrt (pˆq/nˆ) .) , (p^ + z/2 * sqrt (pˆq/nˆ) .

if n increase ,we get compact interval.

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