Answer:
The 99% confidence level (-0.741, -0.659).
Explanation:
The average body mass index (BMI) in a sample of 1559 men was 30.4, with a standard deviation of 0.6.
The average BMI in a sample of 1924 women was 31.1 with a standard deviation of 0.2.
Find a 99% confidence interval for the difference between the mean weights..
The formula for 99% Confidence Interval for difference between the mean weights =
μ is the population mean, and σ is the population standard deviation.
μ1 - μ2 ± z × √σ²1/n1 + σ²2/n2
The z score for 99% confidence interval = 2.576
30.4 - 31.1 ± 2.576 × √0.6²/1559 + 0.2²/1924
-0.7 ± 2.576 × √0.36/1559 + 0.04/1924
-0.7 ± 2.576 × √0.0002309173 + 0.00002079
-0.7 ± 2.576 ×√0.0002517073
-0.7 ± 2.576 × 0.015865286
-0.7 ± 0.04086897674
Hence, the 99% Confidence Interval is
-0.7 - 0.04086897674
= -0.74086897674
≈ -0.741
-0.7 + 0.04086897674
=-0.65913102326
≈ -0.659
Therefore, the 99% confidence level (-0.741, -0.659).