# Stumped again!! Statistics... :(

• Apr 4th 2008, 03:50 PM
darren_a1
Stumped again!! Statistics... :(
Hi guys!

THanks for all your help guys - esp Mr F!

I am stumped on these 2 questions! Any one have any idea on how to proceed?

Assuming the standard deviation for the cost of a bathroom remodel is known to be $545. How large a sample would need to be taken to estimate the mean cost of a bathroom remodel to within$136 with 99% confidence? I got 107 as my answer.

A researcher is interested in estimating the proportion of employees who are unhappy in their current. A prior study estimates this proportion at 0.13. How large a sample would need to be taken to estimate this proportion to within 4% with 95% accuracy? i got 71 as my answer

any help would be appreciated!

Cheers

Sunny
• Apr 4th 2008, 04:55 PM
galactus
The first one is correct. The second one(proportion) should be 272 as the minimum sample size.
• Apr 4th 2008, 04:58 PM
darren_a1
Quote:

Originally Posted by galactus
The first one is correct. The second one(proportion) should be 272 as the minimum sample size.

How do you come up with 272?

Cheers

darren
• Apr 4th 2008, 05:03 PM
galactus
I ran it through my Excel Stats sheet I use for this stuff.

But, here is the 'old-fashioned' way:

$n=pq(\frac{z}{E})^{2}$

p=.13, q=.87, z=1.96, E=.04

$n=(.13)(.87)(\frac{1.96}{.04})^{2}=271.55=272$
• Apr 4th 2008, 05:08 PM
darren_a1
here is what i did!
he z value for the 95% interval is 1.96.

The interval for a proportion is:

mean - sqrt(p(1-p)/N) to mean + sqrt(p(1-p)/N)

We want the sqrt(p(1-p)/N) to be 0.04:

0.04 = sqrt(p(1-p)/N)

p = 0.13

0.04 = sqrt(0.13*0.87/N)

0.04 = sqrt(0.1131/N)

Square:

0.1131/N = 0.0016

Multiply:

0.0016N = 0.1131

Divide:

N = 0.1131/0.0016

N = 70.6875

Round up:

N = 71
• Apr 4th 2008, 05:13 PM
galactus
The formula for sample size in proprotions is as I gave you:

$n=pq(\frac{z}{E})^{2}$

Run it through a calculator. I bet you get 272. I checked this with Excel and my TI-92
• Apr 4th 2008, 05:14 PM
darren_a1
ok!

Thanks for the help! could u look at the other post that i just got going?

cheers

Darren