Respuesta :
Answer:
Step-by-step explanation:
The sample proportion is the point estimate for the population proportion.
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
a) From the information given,
n = 1160
x = 387
p = 387/1160 = 0.33
q = 1 - 0.33 = 0.67
the point estimate of the proportion of the population who would answer yes = 0.33
b) To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.5 = 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, confidence level of 95% is 1.96
Therefore,
Margin of error = 1.96√(0.33)(0.67)/1160 = 0.027
c) the​ 95% confidence interval for the population proportion is
0.33 ± 0.027
The numbers represent the sample proportion and the margin of error
d) The assumptions are
1) the sampling must be random
2) the sample size shouldn't be more than 10% of the population
10/100 × 1160 = 116
387 > 116
3) the sample size should be sufficiently large. That is, greater than 30
387 > 30
