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# Statistics - probability

Thu 3 Mar, 2016 03:37 pm
Our candidate Sanders is waiting for election results. Exit polls show 52% are voting for him. We have a sample of 100 voters and assume a Standard Deviation of 0.497. What is the Probability that his result is just due to luck (that is, the actual voting is 0.50)? What if we have a sample of 1000?
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engineer

2
Thu 3 Mar, 2016 03:47 pm
@jrl06,
I'm not sure what you mean with "assume a Standard Deviation of 0.497".

If the election was a toss up (50% chance for each vote), the expected standard deviation around that is sqrt(100x.50x.50) = 5, so 50 is well within one standard deviation of 52. If you want to compute it by hand, look up a z score of 2/5. If you want to use the Internet, use a favorite binomial calculator and put in a probability of 0.5, 100 trials and 52 hits. The chance of getting 52 or more votes by chance is 39%. The chance of getting 520 votes out of 1000 by chance drops to 10.9%.
jrl06

1
Thu 3 Mar, 2016 04:06 pm
@engineer,
This is a homework question posted by my professor. I'm trying to figure out how to answer it. My assumption is that he wants us to calculate the probability of luck (50/50). He provided the standard deviation - which I've figured out is sqrt P (1-P) = .497
engineer

1
Thu 3 Mar, 2016 09:59 pm
@jrl06,
The standard deviation is sqrt( P (1-P) N ). Since N is 100 (or 1000) you get a much bigger value.
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