Question

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Answer 1

population std dev ,    σ =    4.1000
Sample Size ,   n =    225
Sample Mean,    x̅ =   14.3000

Level of Significance ,    α =    0.05          
'   '   '          
z value=   z α/2=   1.9600   [Excel formula =NORMSINV(α/2) ]      
                  
Standard Error , SE = σ/√n =   4.100   / √   225   =   0.2733
margin of error, E=Z*SE =   1.9600   *   0.273   =   0.536
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    14.30   -   0.536   =   13.7643
Interval Upper Limit = x̅ + E =    14.30   -   0.536   =   14.8357
95%   confidence interval is (   13.76   < µ <   14.84   )