Solution :
Given that,
a) Point estimate = sample proportion = = x / n = 373 / 500 = 0.7460
1 - = 1 - 0.7460 = 0.2540
Z/2 = Z0.025 = 1.96
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 1.96 (((0.7460 * 0.2540) / 500)
= 0.0382
A 95% confidence interval for population proportion p is ,
- E p + E
0.7460 - 0.0382 p 0.7460 + 0.0382
( 0.7078 p 0.7842 )
b) Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 1.96 (((0.7460 * 0.2540) / 500)
= 0.0382
c) correct option is = B. smaller
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