confidence interval help!!!!

**tooshka** · November 17th 2008, 02:51 PM

how do you find a confidence interval without knowing the mean or standard deviation?!

If it helps, here is the question being asked
"construct a 95% confidence interval for the following:
N=100
N=1,000
N=10,000
Use a sample proportion of .4 throughout."

**Aryth** · November 18th 2008, 10:38 AM

Use the following equations:

$p \approx \hat{p} = 0.4$

$CI = \hat{p}\pm z_{\frac{\alpha}{2}}\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$

All we need to find now is $z_{\frac{\alpha}{2}}$

We are given 0.95, so we just use the following:

$(1 - \alpha) = 0.95$

$\alpha = 0.05$

This is a common alpha, and has the corresponding $z_{\alpha}$ and $z_{\frac{\alpha}{2}}$ values:

$z_{\alpha} = 1.645$

$z_{\frac{\alpha}{2}} = 1.96$

All you do now is plug and go.

I'll do the n = 100 for you:

$CI+ = 0.4 + 1.96\sqrt{\frac{0.4(0.6)}{100}}$

$CI+ = 0.4 + 1.96\frac{\sqrt{0.24}}{10}$

$CI+ = 0.4 + 1.96\frac{0.49}{10}$

$CI+ = 0.4 + 1.96(0.049)$

$CI+ = 0.4 + 0.0964 = 0.4964$

$CI- = 0.4 - 0.0964 = 0.3036$

So, your CI is between 30.3 and 49.64 percent.

Just do this again for 1000 and 10000.

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