Question

If n=160 and ˆpp^ (p-hat) =0.28, find the margin of error at a
90% confidence level

Give your answer to three decimals

Answer #1

Solution :

Given that,

n = 160

Point estimate = sample proportion = = 0.28

1 - = 1 - 0.28 = 0.72

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_{/2}
= Z _{0.05} = 1.645

Margin of error = E = Z_{
/ 2} *
((
* (1 -
)) / n)

= 1.645 * (((0.28 * 0.72) /160 )

E = 0.058

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