Answer:
The 95% confidence interval for the difference in the percentages = [19.75, 28.25]
Step-by-step explanation:
The formula for confidence interval for difference in percentages =
p1 - p2 ± z x √[p1(100 - p1)/n1 + p2(100 - p2)/n2)
From the above question:
p1 = 59%
n1 = 1000
p2 = 35%
n2 = 1000
z = z score of the 95% confidence interval = 1.96
Confidence interval = p1 - p2 ± z x √[p1(100 - p1)/n1 + p2(100 - p2)/n2)
= 59 - 35 ± 1.96 × √[59(100 - 59)/1000] + [35(100 - 35)/1000]
= 24 ± 1.96 × √ [59 × 41/1000] + [35 × 65/1000]
= 24 ± 1.96 × √[2419/1000 + 2275/1000]
= 24 ± 1.96 × √2.419 + 2.275
= 24 ± 1.96 × √(4.694)
= 24 ± 1.96 × 2.1665641001
= 24 ± 4.2464656363
Confidence Interval = 24 ± 4.2464656363
24 - 4.2464656363 = 19.753534364
Approximately = 19.75
24 + 4.2464656363 = 28.2464656363
Approximately = 28.25
Therefore, the 95% confidence interval for the difference in the percentages = [19.75, 28.25]
