Question about Sample Size and Margin of Error

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Frank West

Let's say you win at some particular gambling event 600 times out of
1000 trials. I've heard for a sample of that size your margin of
error is around 3%. Therefore for the next 1000 trials you should be
successful between 57% and 63% of the time. Correct?

How do you calculate margin of error? How do they do it for example
in surveys and polls?

Assuming my facts are correct in the above example, what would be your
margin of error over 100, or 10,000 trials? How do you calculate
that?

Thanks,

Frank West
 
Frank West -
Let's say you win at some particular gambling event 600 times out of 1000
Click to expand...
trials. I've heard for a sample of that size your margin of error is around
3%. Therefore for the next 1000 trials you should be successful between 57%
and 63% of the time. Correct? <

Yes, there's approximately a 95% chance that the proportion of wins will be
between 57% and 63%.
How do you calculate margin of error? How do they do it for example in
Click to expand...
surveys and polls? <

Standard error of sample proportion = (p*(1-p)/n)^0.5, where p is sample
proportion and n is sample size. Standard error is "typical variation" from
sample to sample.

Margin of error is usually two standard errors, so based on normal
approximation there's approximately a 95% chance of getting a sample
proportion within two standard errors.

For your example, n=1000 and p=0.6, so standard error is 0.015492, i.e.,
1.5%, and margin of error is 3%.
Assuming my facts are correct in the above example, what would be your
Click to expand...
margin of error over 100, or 10,000 trials? How do you calculate that? <

For n=100 and p=0.6, margin of error is 2*(0.6*0.4/100)^0.5 = 10%.

For n=10,000 and p=0.6, margin of error is 2*(0.6*0.4/10000)^0.5 = 1%.

- Mike Middleton, www.usfca.edu/~middleton
 
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