Solution :
Given that,
a)
n = 100
Point estimate = sample proportion = = 0.90
1 - = 0.10
At 90% confidence level the z is ,
= 1 - 90% = 1 - 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
Z/2 = Z 0.05 = 1.645
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 1.645 * (((0.90 *0.10) / 100)
= 0.049
b)
n = 200
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 1.645 * (((0.90 *0.10) / 200)
= 0.035
c)
n = 260
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 1.645 * (((0.90 *0.10) / 260)
= 0.031
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