Answer:
90% Confidence Interval for difference in Proportion = (-0.106, -0.034)
Step-by-step explanation:
The formula for difference in proportions is given as:
p1 - p2 ± z × √p1(1 - p1)/n1 + p2(1 - p2)/n2
p = x/n
In a 2017 pre-Hurricane Irma
survey, 486 out of 1,080 adults answered in the affirmative.
x1 = 486
n1 = 1080
p1 = 486/1080 = 0.45
In a 2017 post- Hurricane Irma survey, 546 out of 1,050 answered affirmatively.
x2 = 546
n2 = 1050
p2 = 546/1050 = 0.52
Z score for 90% confidence interval = 1.645
Confidence Interval
=0.45 - 0.52 ± 1.645 × √0.45 (1 - 0.45)/1080 + 0.52(1 - 0.52)/1050
= -0.07 ± 1.645 × √0.0002291667 + 0.0002377143
=-0.07 ± 1.645 × √(0.000466881)
= -0.07 ± 1.645 × 0.0216074293
= -0.07 ± 0.0355442212
Confidence Interval
-0.07 - 0.0355442212
= 0.1055442212
Approximately = -0.106
-0.07 + 0.0355442212
= -0.0344557788
Approximately = -0.034
Therefore, 90% Confidence Interval for difference in Proportion = (-0.106, -0.034)
