Question

In: Statistics and Probability

If you had found a 90% confidence interval for µ, how would it have differed from...

If you had found a 90% confidence interval for µ, how would it have differed from the 95% confidence interval?

Expert Solution

The confidence interval is obtained by calculating .

The critical value depends on the confidence level .

If confidence level increases from 90 % to 95 %, will vary from to and hence critical value will become large.

If the critical value increase, then the width of interval will increase or you will get a wider confidence interval.

That means 95% confidence interval will be wider than 90% confidence interval.

For example, suppose we are using the Z- statistics- population is normally distributed with known variance .

If we have sample of size n, then the standard error will be

In that case the critical value of 90% confidence interval will be

The critical value for 95% confidence interval will be .

So width of 90% confidence interval will be

width of 95% confidence interval will be

We can see that width of 95 % confidence interval is more than that of 90% confidence interval.

orchestra answered 2 years ago

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