Find a sample size (n)?

👨🏻‍🏫 學術台數學

Shan

2010-06-12 12:26 pm

I have met a statistics question that, I think, is somewhat difficult, could any one help me?

The question asks:
"How large a sample (n) is required if we want to be 95% confident that a sample proportion (ps) will not differ from the population proportion (p) by more than 0.02?'

Pls help me solve the question step by step with clear illustration.

Thanks so much in advance

更新1:

Given that the sample proportion (ps) is 0.32

回答 (1)

cidyah

2010-06-12 4:55 pm

✔ 最佳答案

It is given that the sample proportion (ps) is 0.32.

Standard deviation of sample proportion = sqrt[p(1-p)]
= sqrt [ (0.32)(1-0.32)] = sqrt[(0.32)(0.68)]= sqrt[0.2176] =0.466476

Sample size n = [ z sd / e] ^2

z=1.96 for a 95% confidence (from normal probability table)
sd = 0.466476 (standard deviation of sample proprtion)
e= 0.02 (error)

Sample size n = [ (1.96) (0.466476) / 0.02 ]^2
n= 2089.8
n = 2090

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