# Thread: sample size & confidence interval...?

1. ## sample size & confidence interval...?

The question is to explain why increasing the sample size the confidence interval will be narrower?

Any help is appriciated

2. What's the formula for calculating the confidence interval? How is that related to n?

3. Calculating a confidence interval for the mean requires the following formula:

estimated mean +/- Z * sqrt[V(Mean)]

As you can see the variance of the mean (variance if the statistic) is closely related with the confidence interval. If you look at it carefully, you'll see that as the variance increases the confidence interval gets wider.

So there is no direct relationship with the sample size. The issue here is that the variance of the mean is indeed closely related to the sample size. Remember that the variance for the mean has the following form:

V(Mean)=(sigma^2)/n

It is easy to see that the bigger n, the smaller variance you'll have. And since smaller variance means a narrower confidence interval, this indirect relationship should be clear.

I hope this boring explanation helps

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