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

Grace Agate

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#

Standard Error #SE=sigma/sqrtn=7.5/sqrt20=7.5/4.47=1.68#

Critical Value for 90% confidence #z=1.64#

#mu=barx+- z .SE# #mu=121.4+- (1.64 xx 1.68)# #mu=121.4+- 2.76#

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#

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Answer 2

Dominic Amato

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.