Question

Here are summary statistics for randomly selected weights of newborn​ girls: n=164​, x=28.7 ​hg, s=6.3 hg. Construct a confidence interval estimate of the mean. Use a 95​% confidence level. Are these results very different from the confidence interval 28.0< μ <29.8 hg with only 19 sample​ values, x=28.9 ​hg, and s=1.8 ​hg?

What is the confidence interval for the population mean?

Answer 1

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   163          
't value='   tα/2=   1.9746   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   6.3000   / √   164   =   0.4919
margin of error , E=t*SE =   1.9746   *   0.4919   =   0.9714
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    28.70   -   0.971411   =   27.7286
Interval Upper Limit = x̅ + E =    28.70   -   0.971411   =   29.6714
95%   confidence interval is (   27.7 < µ <   29.7 )

Yes, because the confidence interval limits are not similar.