Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.

QUESTION

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

See the explanation below.

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 - 2sigma < x < mu + 2sigma ] is about 0.68 Pr[mu-3sigma < x < mu + 3sigma] 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.