Question

14. In a month-long randomized comparative experiment, participants were

Answer 1

Answer: A

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 success

n = number of samples

For the first 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 = 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 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.005 = 0.995

The z score corresponding to the area on the z table is 2.576. Thus, the z score for 99% confidence level 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

Confidence interval = 0.7 - 0.4 ± 0.26

= 0.3 ± 0.26

Option A is correct