Question

A random sample of 24 recent birth records at the local hospital was selected. In the sample, the average birth weight was 119.6 ounces. Population standard deviation was 6.7 ounces. Assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with mean μ. A 95% confidence interval for the population mean birth weight based on these data is

Answer 1

Solution:
Given in the question
Number of sample(n) = 24
Sample mean (Xbar) = 119.6
Population standard deviation () = 6.7
Confidence level = 0.95
level of significance = 1 - Confidence level = 1 - 0.95 = 0.05, alpha/2 = 0.025
From Z table we found Zalpha/2 = 1.96
birth weights follow a Normal distribution, with mean μ
So 95% confidence interval for the population mean birth weight based on these data can be calculated as
Mean +/- Zalpha/2 * /sqrt(n)
119.6 +/- 1.96*6.7/sqrt(24)
119.6 +/- 2.68
So 95% confidence interval is 116.92 to 122.28
We are 95% confident for the population mean birth weight based on these data is between 116.92 ounces to 122.28 ounces