Interval estimates?

Apr 2010
3
0
An interval estimate for the average distance "lifetime" for car tyres was reported to be 34121 kilometres to 38455 kilometres, based on a sample of 66 tyres. The variance of the lifetime was determined from previous studies to be 51124695 kms sqd. What level of confidence can be attributed to this interval estimate? State your answer as a percentage correct to two decimal places.

I know this is a reverse type question but the only examples i've seen how to do this involves being given a true proportion estimated to be between 20% to 30%. I'm not sure how to do my question using that formula as i'm given kilometers rather than percentages. Any help would be appreciated. Thanks.
 

pickslides

MHF Helper
Sep 2008
5,237
1,625
Melbourne
First find the mean and standard deviation.

Do you know these?
 
Apr 2010
3
0
Standard deviation will be 7150.153495 based off the variance, but i'm not sure how to find the mean based on what i'm given
 

pickslides

MHF Helper
Sep 2008
5,237
1,625
Melbourne
i'm not sure how to find the mean based on what i'm given
Will be half way between the given interval.

Then use

\(\displaystyle 38455 = \bar{x}+ Z_{\frac{\alpha}{2}}\times \frac{s}{\sqrt{n}}\)

To solve for \(\displaystyle Z_{\frac{\alpha}{2}}\) you should then be able to work out the level of confidence.