Question

A previous random sample of 4000 U.S. citizens yielded 2250 who are in favor of gun control legislation. How many citizens would need to be sampled for a 90% confidence interval to estimate the true proportion within 2%? Right-click the link to use this Z-table.

Answer 1

(OR)............THIS IS ALSO CORRECT...

Solution :

Given that,

n = 4000

x = 2250

= 2250 / 4000 = 0.5625

1 - = 1 - 0.5625 = 0.4375

margin of error = E = 2% = 0.02

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.645 / 0.02)2 * 0.5625 * 0.4375

= 1664.83

= 1665

1665 citizens would need to be sampled .

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