Mean=33,820.21 Standard Deviation=22,948.45 n=52 Calculate a 99% confidence interval, assuming that sigma is unknown.

Mean=33,820.21

Standard Deviation=22,948.45

n=52

Calculate a 99% confidence interval, assuming that sigma is unknown.

Solutions

Expert Solution

Level of Significance ,    α =    0.01
degree of freedom=   DF=n-1=   51
't value='   tα/2=   2.6757   [Excel formula =t.inv(α/2,df) ]

Standard Error , SE = s/√n =   22948.4500   / √   52   =   3182.3774
margin of error , E=t*SE =   2.6757   *   3182.3774   =   8515.1580

confidence interval is
Interval Lower Limit = x̅ - E =    33820.21   -   8515.158045   =   25305.0520
Interval Upper Limit = x̅ + E =    33820.21   -   8515.158045   =   42335.3680
99%   confidence interval is (   25305.05   < µ <   42335.37   )

milcah answered 1 month ago

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