Answer:
Step-by-step explanation:
1) The point estimate, p for the proportion of college graduates among women who work at home is
p = x/n
Where
x = number of success = 158
n = number of samples = 514
p = 158/514 = 0.307
2) 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
Probability of success, p = 42/100 = 0.42
Probability of failure = 1 - p = 1 - 0.42 = 0.58
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.8 = 0.2
α/2 = 0.2/2 = 0.1
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.1 = 0.9
The z score corresponding to the area on the z table is 1.282. Thus, the z score for a confidence level of 80% is 1.282
Margin of error = 1.282 × √(0.42 × 0.58)/514
Margin of error = 0.028
Therefore, the 80% confidence interval is
0.307 ± 0.028
The lower limit of the confidence interval is
0.307 - 0.028 = 0.279
The upper limit of the confidence interval is
0.307 + 0.028 = 0.335
Therefore, an 80% confidence interval for the proportion of women who work at home is between 0.279 and 0.335
- reflexive property;
- given