Answer:
Step-by-step explanation:
Confidence interval is written 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
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 200
x = 34
p = 34/200 = 0.17
q = 1 - 0.17 = 0.83
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.82 = 0.18
α/2 = 0.18/2 = 0.09
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.09 = 0.91
The z score corresponding to the area on the z table is 1.35. Thus, the z score for a confidence level of 82% is 1.35
Therefore, the 82% confidence interval is
0.17 ± 1.35√(0.17)(0.83)/200
Confidence interval is 0.17 ± 0.036
