Many people think that a national lobby's 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 95% confidence interval was desired to estimate the true proportion to within 2%?
Select one:
a. 2498
b. 2401
c. 2209
d. 2364
Solution :
Given that,
n = 4000
x = 2250
Point estimate = sample proportion = = x / n = 0.5625
1 - = 0.4375
margin of error = E = 0.02
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2 = Z0.025 = 1.96
sample size = n = (Z / 2 / E )2 * * (1 - )
= (1.96 / 0.02)2 * 0.5625 * 0.4375
= 2363.48
sample size = 2364
Option d. is correct.
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