# Why is a 90% confidence interval narrower than a 95% confidence interval?

##### 1 Answer

See the explanation below.

#### Explanation:

The answer is with particular reference to the Normal distribution.

A test procedure starts with fixing the level of significance at 5% or 10% or 1% and so on.

When we say that level of significance is 5%, we admit that our results are likely to be erroneous in 5% cases. That is why a test procedure with 5% level of significance reflects a 95% confidence interval.

From the area table of a standard normal curve, we find that Pr [#mu# -#sigma# < x <#mu# +#sigma# } is about .30

Pr[#mu# - 2#sigma# < x <#mu# + 2#sigma# ] is about 0.68

Pr[#mu# -3#sigma# < x <#mu# + 3#sigma# ] is about 0.95 and so on.

Here we see that as the probability on the right hand side increases, the interval widens and as it decreases, the interval narrows down.

. Hence the 90% confidence interval is narrower than 95% confidence interval.