Question

Here are summary statistics for randomly selected weights of newborn​ girls: n=181, x overbar=28.7 ​hg, s=7.1 hg. Construct a confidence interval estimate of the mean. Use a 90%

confidence level. Are these results very different from the confidence interval 27.1hg<μ <29.5 hg with only 17 sample​ values,

x overbar=28.3 ​hg, and =2.8 ​hg?

What is the confidence interval for the population mean μ​?

__ hg <μ<___ hg ​(Round to one decimal place as​ needed.)

Answer 1

GIVEN:

Sample size

Sample Mean

Sample standard deviation

CONFIDENCE INTERVAL:

The formula for ​% confidence interval for population mean when standard deviation is unknown is given by,

where ​ is the t critical value at desired confidence level with ​ degrees of freedom.

90% CONFIDENCE INTERVAL FOR POPULATION MEAN:

Thus the formula for 90% confidence interval for population mean is given by,

where ​ is the t critical value at 90% confidence level with ​ degrees of freedom.

Thus .

Now

Thus the 90% confidence interval is ​. Thus we are 90% confident that the true population mean lies between and . And we could see that this is different from the confidence interval with only 17 sample​ values, and ​.