Sample Size

Would like to learn the correct technique to caculate sample sizes. We are working with truck tires and determining the number of miles we get from multiple brands. We know brand x reaches 24,000 miles but we would like to reach 34,000 miles through our testing. We will have 3 types of tires in the study. How many tires do we have to measure to be 95% confident of our findings? Thanks for all your help!!!
Formula I've been given includes the Z value for confidence, sigma and margin of error. No reference to power. Results in about 1/2 the sample size. Mathematically I see why but which is better to work with? Seems a few assumptions that makes the results questionable, like sigma value. Are there other examples I could review?


TS Contributor
The formula you refer to assumes that the population standard deviation is known, or that you have a very, very good estimate of it.

The formula in my example assumes that the estimation of sigma is little more than a guess, or perhaps derived from previous data...

Personally, I would go with my formula, since it's a bit more conservative, but if you're really sure about your estimate of sigma, then your formula may be OK.

Disclaimer: In my experience, sample size is determined more by economic factors than by statistical precision factors.
I have collected the result of bone scan for 30 patients and also thier blood inflammatory marker and clinical score and I would like to do prospective study to correlate between the clinical diagnosis and the Bone scan diagnosis, to see how useful Bone scan in diagnosis.