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If n=410 and ˆp (p-hat) =0.32, find the margin of error at a 99% confidence level...

If n=410 and ˆp (p-hat) =0.32, find the margin of error at a 99% confidence level

=_____________ Give your answer to three decimals

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that,

n = 410

Point estimate = sample proportion = =0.32

1 - = 1 - 0.32 = 0.68

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576 * (((0.32*0.68) / 410)

= 0.059

The margin of error is 0.059

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