Answer:
The 99% confidence interval for the true difference between the mean numbers of hours of sports watched per week for the two regions is = [ CI [-0.254, 0.654].
Explanation:
The confidence interval for the true difference between the mean formula is given as:
μ1 - μ2 ± z × √(σ²1/n1 + σ²2/b2)
μ1 = Mean 1 = 4.5 hours
μ2 = Mean 2 = 4.7 hours
z = z score for 99% confidence interval = 2.576
σ1 = Standard deviation 1(South) = 1.5 hours
σ2 = Standard deviation 2(North) = 1.7 hours
n1 = number of samples 1 = 195
n2 = number of samples 2 = 148
Confidence Interval
= 4.5 - 4.7 ± 2.576 × √1.5²/195 + 1.7²/148
= 0.2 ± 2.576 × √0.0115384615 + 0.019527027
= 0.2 ± 2.576 × √0.0310954885
=0.2 ± 0.4542495969
Confidence Interval
= 0.2 - 0.4542495969
- 0.2542495969
= -0.254
Approximately = -0.654
= 0.2 + 0.4542495969
= 0.6542495969
Approximately = 0.654
Hence, The 99% confidence interval for the true difference between the mean numbers of hours of sports watched per week for the two regions is = CI [-0.254, 0.654].]