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 = 536
p = 37/100 = 0.37
q = 1 - 0.37 = 0.63
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.005 = 0.995
The z score corresponding to the area on the z table is 2.53. Thus, confidence level of 99% is 2.58
Therefore, the 99% confidence interval is
0.37 ± 2.58 × √(0.37)(0.63)/536
= 0.37 ± 0.054
The lower limit of the confidence interval is
0.37 - 0.054 = 0.316
The upper limit of the confidence interval is
0.37 + 0.054 = 0.424
Therefore, with 99% confidence interval, the proportion of all teenagers that want more discussions with their parents about school is between 0.316 and 0.424
