How to find Confidence interval

[BCCB]

A researcher surveys 25 people and finds that their average commute is 15 minutes with a standard deviation of 1.5 minutes. Calculate the 95 percent confidence interval on variance. Do most people have a commute of 20 minutes?

Confidence interval for variance? should I just use the variance instead of the standard deviation? so 1.5^2=2.25

root 25= 5

15+1.962.255 and 15−1.962.255
15+0.882 and 15−0.882

15.88,14.12

so, no , most people will not have a commute of 20 minutes

Is this right?

Thanks!

 

[Simon Bridge]

I don't follow your reasoning.

You need to clarify what you are testing ... identify the question the confidence interval is supposed to be used to answer.

It looks like you want to know if at least 50% of people have a commute of 20mins - based on your sample of 25 out of a large population.

You also want to figure what the confidence interval on variance has to do with figuring this out.
http://www.milefoot.com/math/stat/ci-variances.htm

 

[Stephen Tashi]

It's likely that nobody has a commute of exactly 20 minutes.

If you want to know if most people in the sample have a commute of 20 minutes or more, you could try using Chebyshev's inequality - i.e. by considering "the sample" to be the same as "the population".