Question

Many people think that a national lobbyʹs successful fight against gun control legislation is reflecting the will of a minority of Americans. A previous random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. How many citizens would need to be sampled if a 99% confidence interval was desired to estimate the true proportion to within 5%

Answer 1

The minimum sample for the given margin of error at 95% confidence level is computed as:

Where E is the margin of error given as 5% or 0.05 in proportion. Also, a previous random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. Hence the sample proportion would be:

and at a 95% confidence level the Zc is computed using the excel formula which is =NORM.S.INV(0.975), thus the Zc is computed as 1.96.

Now the minimum sample is calculated as;

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