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 = 700
x = 46
p = 46/700 = 0.066
q = 1 - 0.066 = 0.934
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.95
The z score corresponding to the area on the z table is 1.645. Thus, the z score for a confidence level of 90% is 1.645
Therefore, the 90% confidence interval is
0.066 ± 1.645√(0.066)(0.934)/700
= 0.066 ± 0.0094
The lower limit of the confidence interval is
0.066 - 0.0094 = 0.0566
The upper limit of the confidence interval is
0.066 + 0.0094 = 0.0754
