In: Statistics and Probability
If you had found a 90% confidence interval for µ, how would it have differed from the 95% confidence interval?
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.