Answer:
The 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program = ( -0.293, 0.023)
Explanation:
The formula for confidence interval for the difference between the proportions is given as:
p1 - p2 ± z × √p1 (1 - p1)/n1 + p2(1 - p2)/n2
From the question
We have two groups.
Group 1 = For women
A survey found that 37 of 74 randomly selected women
p1 = x/n1
n1 = 74
x1 = 37
p1 = 37/74
p1 = 0.5
Group 2 = For Men
A survey found out that 47 of 74 randomly selected men follow a regular exercise program
p2 = x/n1
n2= 74
x2 = 47
p2 = 47/74
p2 = 0.6351351351 ≈ 0.635
z = z score for 95% Confidence Interval = 1.96
The confidence interval for the difference between the proportions is given as:
p1 - p2 ± z × √p1 (1 - p1)/n1 + p2(1 - p2)/n2
0.5 - 0.635 ± 1.96 × √0.5 (1 - 0.5)/74 + 0.635(1 - 0.635)/74
-0.135 ± 1.96 × √(0.5 × 0.5)/74 + (0.635× 0.365)/74
-0.135 ± 1.96 × 0.08068750209663572
-0.135 ± 0.158147504109406
Hence:
= -0.135 - 0.158147504109406
= -0.2931475041
Approximately = -0.293
= -0.135 + 0.158147504109406
= 0.0231475041
Approximately = 0.023
Therefore, the 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program = ( -0.293, 0.023)