# sample size

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• #39123

ong
Member

A political pollster wants to estimate the proportion of voters who will vote for the Democratic candidate in a presidential campaign. The pollster wants to have 90% confidence that her prediction is correct to within + – 0.04 of the population proportion.
(a) what sample size is needed?
(b) if the pollester wants to have 95% confidence, what sample size is needed?
(c)if she wants to have 95% confidence and a sampling error of +-0.3, waht sample size is needed?
(d) on the basis of your answers to (a)- (c), what general conclusion can be reached about the effect of the confidence level desired and acceptable sampling error on the sample size need? dicuss.

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#118324

Schuette
Participant

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#118327

Whitehurst
Participant

When sample data is collected and the sample mean is calculated, that sample mean is typically different from the population mean . This difference between the sample and population means can be thought of as an error. The margin of error is the maximum difference between the observed sample mean and the true value of the population mean :

where:
is known as the critical value, the positive value that is at the vertical boundary for the area of in the right tail of the standard normal distribution.
is the population standard deviation.
is the sample size
Rearranging this formula, we can solve for the sample size necessary to produce results accurate to a specified confidence and margin of error.

Work on it and I think that will give your answers to all your questions !! Good Luck!!!

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#118332

Ken Feldman
Participant

He can work on this all day long and won’t get the correct answer.  Unless you are being really deep in your guidance, you need to check the stat book again as well.  The poster is asking about sample size for proportions.  You gave him a generalized formula consistent with continuous data.  If you finished by advising him to substitute parameter measures for a binomial distribution you would be correct.  As it stands now you are WRONG.

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#118335

Ruddy
Participant

OK, then please tell us how to calculate it if you disagree this regular way ? thanks

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#118342

Mikel
Member

105.6853

150.0568

266.7676

Figure out d) on your own.

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#118347

Obiwan
Participant

It is not a question of the “regular” way…it is a question of the type of data.  The type of data plays deeply into the calculation for the sample size!  For a simple formula…
Well, I thought I could paste the formula in here, but could not figure out how!  (Any suggestions would be appreciated!)…so here is a reference for you:
Montgomery, D.C., Runger, G.C. & Hubele, N.F. (2001).  Engineering Statistics, 2nd Ed.  New York: John Wiley and Sons.
Look at page 198…and you too can calculate this!
Obiwan

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#118349

Ken Feldman
Participant

By the tone of your reply, I think it would be a waste at this point to answer your question.  It is a simple matter of looking up the calculation for sample size FOR A PROPORTION.  It means you would need to understand the difference between continuous and discrete data and the fact that the discrete data comes from a Binomial distribution.  Once you understand the parameters for the mean and s.d. of a binomial distribution, the answer will become obvious.

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