
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 28th, 2015, 07:36 AM  #1 
Newbie Joined: Nov 2015 From: HK Posts: 8 Thanks: 0  sample size for confidence interval of proportion
Question: A state legistlator wishes to survey residents of her district to see what proportion of the electorate is aware of her position on using state funds to pay for abortions. What sample size is necessary if the 95% confidence interval for p is to have width at most 0.10 irrespective of p? (p bar) + Z0.025 sigma/sqrt(n)  (p bar  Z0.025 sigma / sqrt(n)) <= 0.1 2(Z0.025 sigma/ sqrt(n) ) <= 0.1 but sigma is not known 
November 28th, 2015, 07:44 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
That's not the correct formula for sample proportions. You should refer to your textbook/lecture notes again... The formula is like this: $\displaystyle \hat{p} \pm z_{\alpha / 2} \sqrt{\frac{\hat{p}(1\hat{p})}{n}} $ since the variance of $\displaystyle \hat{p}$ is approximated by $\displaystyle \frac{\hat{p}(1\hat{p})}{n}$ (true variance is $\displaystyle \frac{p(1p)}{n}$). Out of curiosity, is this HKDSE M1 or tertiarylevel? Last edited by 123qwerty; November 28th, 2015 at 07:47 AM. 
November 28th, 2015, 08:04 AM  #3  
Newbie Joined: Nov 2015 From: HK Posts: 8 Thanks: 0  Quote:
It is tertiary level  
November 28th, 2015, 05:55 PM  #4  
Newbie Joined: Nov 2015 From: HK Posts: 8 Thanks: 0  Quote:
 
November 28th, 2015, 06:02 PM  #5 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics  
November 28th, 2015, 11:54 PM  #6 
Newbie Joined: Nov 2015 From: HK Posts: 8 Thanks: 0  
November 29th, 2015, 07:22 AM  #7 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics  We take the largest possible value of $\displaystyle \hat{p}(1\hat{p})$. Let f(x) = $\displaystyle \hat{p}(1\hat{p})$. Then f'(x) = $\displaystyle 2\hat{p}  1$. $\displaystyle 2\hat{p}  1 = 0$ at $\displaystyle \hat{p} = 0.5$, so we assume this value.

November 29th, 2015, 11:08 PM  #8 
Newbie Joined: Nov 2015 From: HK Posts: 8 Thanks: 0  where does " f'(x) = 2p̂ −1. 2p̂ −1=0" come from?

November 30th, 2015, 05:20 AM  #9 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics  
November 30th, 2015, 06:16 AM  #10 
Newbie Joined: Nov 2015 From: HK Posts: 8 Thanks: 0  

Tags 
confidence, interval, proportion, sample, size 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
sample size for confidence interval  tttim  Probability and Statistics  1  November 28th, 2015 02:50 PM 
sample proportion of the sample mean  shivadiva  Advanced Statistics  0  April 30th, 2013 07:46 PM 
sample size and confidence interval  mikeportnoy  Algebra  1  March 14th, 2012 12:42 PM 
Sample Size and Std Dev  jskrzy  Algebra  1  November 16th, 2011 04:17 PM 
Confidence Interval  Seems to wide, sample size?  kerrymaid  Advanced Statistics  1  June 11th, 2010 05:25 AM 