Any Prob and Stats folks around?

[Syberus]

So I'm trying to help this person do their prob and stats homework.. but they have a different teacher than I do, and learned different stuff in class so it's kind of hard going. I can hammer anything out if given a formula, but the person wasn't able to come up with one for this problem.. so I was wondering if any of you smart people out there could do me a favor and throw it out (or the answer with it if you're feeling generous)


Lung cancer is the leading cause of cancer deaths in both men and women in the United States, China, and Canada. In several other countries, lung cancer is the number one cause of cancer deaths in men and the second or third among women. Obly about 14% of all people who develop lung cancer survive for five year

Suppose you wanted to see if this survival rate were true. How large a sample would you need to estimate the true proprotion surviving for five years after diagnosis to within 1% with 95% confidence? (use 14% as the value of p)


I can do Confidence Intervals without incident.. but I have no clue how to figure out how large your sample size needs to be in order for a probabilty to be true.

[Alarke]

Giving the best thought i have on the situation, so here goes:

When you're trying to figure out what sample size to use (i THINK that's what you're asking) you use the formula:

n = p(1-p)((Z sigma/2)/B)^2

So if p = .14 and 95% confidence leaves you with a Z of .05/2 = .025 ... a Z score of .025 = 1.96.. and if you need to know within 1% that leaves you with an error bound of 1% (.01)


n = .14(1-.14)(1.96/.01)^2 = 4625.28, which rounds to 4626 people

[Alarke]

Hope that works, and hope that helps. If not, it's your own fault for listening to me! mwahaha

[GSLeloo]

Karl Pearson once tossed a coin 24,000 times and recorded 12,012 heads. A) Calculate the point estimate for p=p(head) based on Pearson's results. B) Determine the standard error of proportion. C) Determine the 95% confidence interval estimate for p=P(Head)


Just putting that one up if someone is bored and can answer it before 1:20 so that you know I don't end up crying again realizing I am failing a class for the first time ever... that's a bit of a babble.

[Syberus]

That's what my roomate said too alarke, but then there was a chart in the book that said if you want to be within 1% for a 95% interval you should use 10,000 people so.. I have no idea haha

[Alarke]

I've never seen any chart about how many people to be within 1%, but that is deffinatly the formula to find the population needed in order to determine a successful hypothesis test with those numbers, oh well. And Leloo, know it's a little late, but all you do is take

12012/24000 = .5005 so you use that for your p, and then set it up exactly the same as the last formula that i put here.