Answer:
Step-by-step explanation:
Confidence interval for population proportion is expressed as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
From the information given,
Sample proportion, p = 65/100 = 0.65
q = 1 - 0.65 = 0.35
n = 200
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, the z score for a confidence level of 95% is 1.96
Margin of error = 1.96√(0.65)(0.35)/200
Margin of error = 0.066 = 6.6%
The maximum boundary of the interval is
0.65 + 0.066 = 0.716
