Answer:
The 95% confidence interval for the difference of the hours worked is [-0.052 , 0.0012]
Step-by-step explanation:
Formula for Confidence interval based on difference =
p1 - p2 ± z × √[p1(1 - p1)/n1] + [p2(1 - p2)/n2]
p1 = proportion for the first group = x/n
= 8.5/10.2
= 0.8333333333
≈ 0.83
n1 = 1000
p2 = proportion for the second group = 6.9/8.1
= 0.8518518519
≈ 0.85
n2 = 1000
Confidence Interval = p1 - p2 ± z × √[p1(1 - p1)/n1] + [p2(1 - p2)/n2]
= 0.83 - 0.85 ± 1.96 √[0.83(1 - 0.83)/1000] + [0.85(1 - 0.85)/1000]
= -0.02 ± 1.96 × √0.83 × 0.17/1000 + 0.85 × 0.15/1000
= -0.02 ± 1.96 × √0.0001411 + 0.0001275
= -0.02 ± 1.96 × √0.0002686
= -0.02 ± 1.96 × 0.0163890207
= -0.02 ± 0.0321224806
-0.02 - 0.0321224806
= -0.0521224806
≈ -0.052
-0.02 + 0.0321224806
= 0.0121224806
≈ 0.012
Therefore, the 95% confidence interval for the difference of the hours worked is [-0.052 , 0.0012]
