# Statistics with confidence intervals

1. Jun 16, 2009

### war485

1. The problem statement, all variables and given/known data

Suppose the porosity (in %) of samples taken from the ground found to be normally distributed with σ = 0.85 %

What sample size is necessary to estimate the true mean porosity to within 0.25
with 99% confidence?

2. Relevant equations

C.I. = confidence interval = mean +- z*σ*n^(-0.5)
n = (2*z*σ/w)^2
interval width = w
z = 2.575

3. The attempt at a solution

Not really sure what is meant by "... to within 0.25" maybe someone can help clarify this? Is it referring to the confidence interval width? Also, I thought that the confidence intervals do not estimate the true mean. I thought C.I. only estimates whether or not the other samples will have the same mean within the C.I. range.

Last edited: Jun 16, 2009
2. Jun 17, 2009

Usually "to within xxx" refers to the desired margin of error - this would not be the length of the confidence interval, but half the length.

A confidence interval provides a range of values which can be considered "reasonable values" for the true mean (that is highly non-mathematical language, but I think it gets the point across)

3. Jun 17, 2009

### war485

thanks for clarifying the problem statdad.

4. Jun 17, 2009

### EnumaElish

0.25 is the interval width ("w"), which is the same as error margin. This can be interpreted as ±0.25. Since it was not stated as ±0.25 but as 0.25, they probably meant ±0.125.

The 99% C.I. implies a 0.5% probability under either tail, as statdad suggested. You should verify that your z value is consistent with that probability.

Last edited: Jun 17, 2009