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In: Statistics and Probability

Q7. Here are summary statistics for randomly selected weights of newborn​ girls: n=210​, x overbarx=28.9 ​hg,...

Q7. Here are summary statistics for randomly selected weights of newborn​ girls: n=210​, x overbarx=28.9 ​hg, s=6.3hg. Construct a confidence interval estimate of the mean. Use a 99​% confidence level. Are these results very different from the confidence interval 27.0 hgless than

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

____hgless than

Solutions

Expert Solution

std dev , s =    6.3000
Sample Size ,   n =    210
Sample Mean,    x̅ =   28.9000

Level of Significance ,    α =    0.01          
'   '   '          
z value=   z α/2=   2.5758   [Excel formula =NORMSINV(α/2) ]      
                  
Standard Error , SE = s/√n =   6.300   / √   210   =   0.4347
margin of error, E=Z*SE =   2.5758   *   0.435   =   1.120
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    28.90   -   1.120   =   27.7802
Interval Upper Limit = x̅ + E =    28.90   -   1.120   =   30.0198
99%   confidence interval is (   27.8 < µ <   30.0 )


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