Solution :
Given that,
n = 301
x = 187
Point estimate = sample proportion = = x / n = 187 / 301 = 0.621
1 - = 1 - 0.621 = 0.379
At 99.9% confidence level
= 1 - 99.9%
=1 - 0.999 = 0.001
/2
= 0.0005
Z/2
= Z0.0005 = 3.291
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 3.291(((0.621 * 0.379)) / 301)
= 0.092
A 99.9% confidence interval for population proportion p is ,
- E < p < + E
0.621 - 0.092 < p < 0.621 + 0.092
0.529 < p < 0.713
The 99.9% confidence interval for the population proportion p is : 0.529 < p < 0.713
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