Answer: A
Detailed explanation:
The confidence interval for the difference in proportions is represented as
Difference in sample proportions ± margin of error
Sample proportion, p is calculated as x/n
where x denotes the number of successes
and n indicates the total number of samples
For the initial treatment,
x = 35
n1 = 50
p1 = 35/50 = 0.7
For the second treatment,
x = 16
n2 = 40
p2 = 16/40 = 0.4
Margin of error is calculated as z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To find the z score, we subtract the confidence level from 100% to obtain α
α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
This represents the area in each tail. As we are focused on the area in the center, it becomes
1 - 0.005 = 0.995
The z score for this area on the z table is 2.576. Consequently, for a 99% confidence level, the z score is 2.576
Margin of error = 2.576 × √[0.7(1 - 0.7)/50 + 0.4(1 - 0.4)/40]
= 2.576 × 0.10099504938
= 0.26
The confidence interval is calculated as 0.7 - 0.4 ± 0.26
= 0.3 ± 0.26
Thus, Option A is the correct answer