What is a 90% confidence interval for the population mean birth weight based on the data?

Question

An SRS of 20 recent birth records at the local hospital were selected. In the sample, the average birth weight was 121.4 ounces and the standard deviation was 7.5 ounces. I assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with some mean.

I am also interested in a 99% confidence interval for the population mean birth weight. What is the margin of error associated with the confidence interval?

Grace Agate · Accepted Answer

90% confidence interval between 118.64 ounces and 124.16 ounces

99% confidence interval between 117.13 ounces and 125.67 ounces

Given - Mean weight #barx=121.4# Sample size #n=20# Standard Deviation #sigma = 7.5# Birth weight follows Normal Distribution. Standard Error #SE=sigma/sqrtn=7.5/sqrt20=7.5/4.47=1.68# Critical Value for 90% confidence #z=1.64# 90% confidence Interval #mu=barx+- z .SE# #mu=121.4+- (1.64 xx 1.68)# #mu=121.4+- 2.76# With 90% confidence interval, population mean birth weight falls between 118.64 ounces and 124.16 ounces Critical Value for 99% confidence #z=2.54# #mu=barx+- z .SE# #mu=121.4+- (2.54 xx 1.68)# #mu=121.4+- 4.27# With 99% confidence interval, population mean birth weight falls between 117.13 ounces and 125.67 ounces

Dominic Amato · Answer

undefined To calculate a 90% confidence interval for the population mean birth weight, you need to know the sample mean, sample standard deviation, and sample size. Without this information, I can't provide the specific confidence interval. You'll need to provide the data or statistical summary (such as mean, standard deviation, and sample size) to compute the confidence interval. Once you have that information, you can use statistical formulas or software to find the confidence interval.