a)
Solution :
Given that,
n = 800
x = 220
Point estimate = sample proportion = = x / n = 0.275
1 - = 1 - 0.275 = 0.725
At 90% confidence level
= 1 - 90%
= 1 - 0.90 =0.10
/2
= 0.05
Z/2
= Z_{0.05 = 1.645} ( Using z table )
Margin of error = E = Z_{ / 2} * (( * (1 - )) / n)
= 1.645 (( 0.275( 0.725 ) / 800 )
= 0.026
A 90% confidence interval for population proportion p is ,
- E < p < + E
0.275 - 0.026 < p < 0.275 + 0.026
0.249 < p < 0.301
(0.249,0.301)
b)
A 90% confidence interval for the population proportion p (0.249,0.301) is fall between lower bound and upper bound
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