# smaple size for proportions

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• #43542

Shiva
Member

For calulating sample size for proportions when we must use p = 0.5 and q = 0.5 and when must we not use this values.

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#138239

dangwal
Participant

Shiva – p and q are probabilities of success and failures respectively in Bernaulli experiments.
These are known before hand and hence the question when we must use p = 0.5 and q = 0.5 and when must we not use this values. is not correctly phrased one.

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#138240

Ronald
Participant

Shiva-
If you know or can estimate the proportion of the population or have historical data, use the resulting p and q from that in the sample size equation (it will give you a smaller sample size)
If the p is unknown, then use p=0.5 and q=0.5 as the product is the highest possible value of p*q possible (pq=0.25) and will provide a very large sample size due to the fact that p is unknown (prevents under sampling).
Lee

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#138246

Shiva
Member

Hi, Lee
Thanks so much for oyur reply .
I have pasted a question here and the part B is that I got problems with i was wondering if you could help somehow.
In a random sample of 250 Ameicans, 83 claimed to have watched the Football League Grand Final in 2005 on television.
(a) Estimate, with 95% confidence, the true population proportion of americans who watched the Grand Final on television.
b) What sample size is required if we wish to estimate the population proportion of Americans who watched the Grand Final on television to within plus or minus 2% with 99% con dence? Use a conservative method in determining the sample size.

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#138247

Shiva
Member

Hi Nitin,
Thanks so much for oyur reply .
I have pasted a question here and the part B is that I got problems with i was wondering if you could help somehow.
In a random sample of 250 Ameicans, 83 claimed to have watched the Football League Grand Final in 2005 on television.
(a) Estimate, with 95% confidence, the true population proportion of americans who watched the Grand Final on television.
b) What sample size is required if we wish to estimate the population proportion of Americans who watched the Grand Final on television to within plus or minus 2% with 99% con dence? Use a conservative method in determining the sample size.

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#138251

Ken Feldman
Participant

Shiva, Lee already answered your question without doing your problem for you.  Read it again.  If you have some ideas as to the population proportion use it in the formula.  If not, then use p=.5 and q=.5.

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#138268

Nanni
Participant

a) 95% IC = (0.273929, 0.394110)

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#138273

Shiva
Member

Sorry i am bothering again.

But it says to use conservative method which i think is  p = 0.5 but the proportion is given in the question.

So thats where I am confused.

Any help would be apprecaited.

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#138283

Ken Feldman
Participant

Your confusion is justified, it is a poorly written question.  One interpretation of “conservative” might mean assuming you know nothing and using the .5 as your proportion.  Try to seek clarity about what is meant with the term “conservative”.

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#138295

Shiva
Member

Thanks but i did ask!! and nothing of much help.

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#138298

Ken Feldman
Participant

Well, then you will have to deal with the idiot.  Go with your instincts and use the .5 since that is for situations in which you know nothing and will result in the largest sample size.  Still a poorly worded question but answer it and move on.  Good luck.

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#138302

Tim
Member

* The statement only says that 83 “claimed” to have watched — you need to know what proportion of Americans are liars! ;-)* You could just ignore the data and make up your own answer. That seems to be a Conservative approach to issues like global warming. ;-)

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#138304

Shiva
Member

Ya! have to move on still bit of scary buttttttttttttttttttt..
Thanks

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#138305

Ken Feldman
Participant

Word your posts clearly and precisely and don’t ask for help without some effort on your own and you will find this Forum very supportive and knowledgeable.  Also humorous, insulting, cynical, sarcastic but ignoring that, there are some incredible posters on here.  Good luck.

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#138306

Shiva
Member

Thanks.
But I really do try and we discuss but if there is no way out then thought to try the net.

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