Answer:
Step-by-step explanation:
Sample proportion is x/n
Where
p = probability of success
n = number of samples
p = x/n = 63/150 = 0.42
q = 1 - p = 1 - 0.42 = 0.58
To determine the z score, we subtract the confidence level from 100% to get α
Since 1 - α = 0.9
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, confidence level of 90% is 1.645
Confidence interval is written as
(Sample proportion ± margin of error)
Margin of error = z × √pq/n
= 1.645 × √(0.42 × 0.58)/150
= 0.066
The lower end of the confidence interval is
0.42 - 0.066 = 0.354
The upper end of the confidence interval is
0.42 + 0.066 = 0.486
Therefore, the answers to the given questions are
1) d. 0.42
2) the quantity after the ± is the half width. It is also the margin of error. Thus
The half width of this confidence interval is closest to
d. 0.0663
3) c.0.3537
4) b.0.4863
5) d.With 90% confidence, 0.3537 < p < 0.4863
