Answer:
Step-by-step explanation:
Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p = x/n
Where x = number of successes
n = number of samples
For the indians,
x = 368
n1 = 634
p1 = 368/634 = 0.58
For the asians
x = 130
n2 = 567
p2 = 130/567 = 0.23
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 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
Margin of error = 1.96 × √[0.58(1 - 0.58)/634 + 0.23(1 - 0.23)/567]
= 1.96 × √0.00038422713 + 0.00031234568)
= 0.052
Confidence interval = 0.58 - 0.23 ± 0.052
Confidence interval = 0.35 ± 0.052
