Answer:
Step-by-step explanation:
a) The population parameter is the population proportion.
b) 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 = 1028
p = 36/100 = 0.36
q = 1 - 0.36 = 0.64
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.99 = 0.1
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 - 0.05 = 0.995
The z score corresponding to the area on the z table is 2.58. Thus, confidence level of 99% is 2.58
Therefore, the 99% confidence interval is
0.36 ± 2.58 × √(0.36)(0.64)/1028
The lower limit of the confidence interval is
0.36 - 0.039 = 0.321
The upper limit of the confidence interval is
0.36 + 0.039 = 0.399
Therefore, with 99% confidence interval, the proportion of U.S. teens aged from 13 to 17 years old that have a computer with Internet access in their rooms is between 0.321 and 0.399
c) for a margin of error of 1%, that is 1/100 = 0.01, then
0.01 = 2.58 × √(0.36)(0.64)/n
0.01/2.58 = √0.2304/n
0.00387596899 = √0.2304/n
Square both sides
0.00001502314 = 0.2304/n
n = 0.2304/0.00001502314
n = 15336
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