# Confidence interval

• May 5th 2011, 04:40 AM
jabba1
Confidence interval
In a test of the effect of dampness on electric connections, 100 electric connections were tested under damp conditions and 150 were tested under dry conditions. Twenty of the damp connections failed and only 10 of the dry ones failed. Find a 95% confidence interval for the difference between the proportions of connections that fail when damp as opposed to dry.

I am having a very hard time getting through this problem.
• May 5th 2011, 04:56 AM
amul28
what answer did you get?
• May 5th 2011, 05:28 AM
jabba1
i don't know how to start it
• May 5th 2011, 05:38 AM
amul28
95% confidence interval for the difference between the proportions is

$\displaystyle (p_1 - p_2)\pm Z_{\alpha /2}\times \sqrt{\frac{p_1 q_1}{N_1}+\frac{p_2 q_2}{N_2}}$

here your

$\displaystyle p_1=\frac{n_1}{N_1}$

$\displaystyle p_2=\frac{n_2}{N_2}$

$\displaystyle N_1=100, N_2=150$
$\displaystyle n_1=20, n_2=10$
$\displaystyle Z_{\frac{0.05}{2}}=1.96$

So solve accordingly.

PS: Check the correction i made.
• May 5th 2011, 06:47 AM
jabba1
how do i calculate q?

1-p=q
lost my mind for a sec

so i got 1.225, -.5668
does that seem right?
• May 5th 2011, 09:04 PM
amul28
jabba1,

My bad. I guess even you dint realize that i have made a mistake in giving the values for $\displaystyle n_1$ and $\displaystyle n_2$.(Surprised)

And yes $\displaystyle q=1-p$. (Nod)