Question

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

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?

Answer 1

90% confidence interval between 118.64 ounces and 124.16 ounces

99% confidence interval between 117.13 ounces and 125.67 ounces

Explanation:

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