# Why is a 99% confidence interval wider than a 95% confidence interval?…

Why is a 99% confidence interval wider than a 95% confidence interval?

Solution)

The definition of a confidence interval is that it contains the true population mean. If I have a 95% confidence interval, that means I am 95% certain that the true population mean is in the interval. If I want to be even more certain, I have to widen the interval. If I can be less certain, I can narrow the interval.

So the widest interval will be 99%, and the narrowest would be 90%.

Example:

you're trying to figure out where in the city Comet Donuts is in, but you really don't know for sure. A desperately hungry person hands you a map and asks you to show him where it is. If someone forces you to be 99% accurate, are you going to draw a wide or narrow circle on the map? You can't afford to be wrong – at 99% you're saying that you'll be wrong one time out of 100! So you draw a big circle.

If the person asking doesn't even like donuts, they're just asking for the heck of it, you can be 90% accurate, so you can take a chance and draw a small circle. You'll be wrong 10% of the time.

12. A person claims to be able to predict the outcome of flipping a coin. This person is correct 16/25 times. Compute the 95% confidence interval on the proportion of times this person can predict coin flips correctly. What conclusion can you draw about this test of his ability to predict the future?

Solution)

WE HAVE GIVEN THAT n = 25 and p = 16/25

And we need to construct the 95% C.I. for the proportion of times this person can predict coins flips correctly as,

?± 1.96 * v (?q^/n)

=.64± 1.96 * v (.64*.36/25)

= .64 ± .1882

So the 95% C.I. is,

(0.4518, 0.8282)

So We Are 95 Out Of 100 Attempts are confident that the values of the samples are lies b/w (.4518,.8282)

15. You take a sample of 22 from a population of test scores, and the mean of your sample is 60.

(a) You know the standard deviation of the population is 10. What is the 99% confidence interval on the population mean?

Solution)

We have given that n = 22, sample mean =60 and s = 10

The 99% C.I. for the population mean is,

= sample mean ± 2.58 *s /vn

= 60 ± 2.58 * 10 / v22

= 60 ± 5.501

So, (54.499, 65.501)