Solution :
n = 150
x = 106
= x / n = 106 / 150 = 0.707
1 - = 1 - 0.707 = 0.293
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2 = Z0.005 = 2.576
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 2.576 * (((0.707 * 0.293) / 150)
=0.096
A 99% confidence interval for population proportion p is ,
- E < P < + E
0.707 - 0.096 < p < 0.707 + 0.096
0.611 < p < 0.803
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