Question

The Business Association of the Montreal Area (BAMA) wants to estimate the number of hours per week that each business executive in the city works. BAMA found that the following is the number of hours worked weekly in 2019 by a sample of business executives in the Montreal Area:

82	82	80	81	84	85	81	80	79	85	85	75

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1. What is the point estimate of the population mean? (Round your answer to 2 decimal places.)

2. Develop a 90% confidence interval for the population mean. (In your calculations, use 2 decimal places for the mean and 3 decimal places for other values. Round your final answers to 2 decimal places.)

Answer 1

a)

Sample Size ,   n =    12
point estimate of population mean , x̅ = ΣX/n =    81.58

b)

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   2.9683
Level of Significance ,    α =    0.1          
degree of freedom=   DF=n-1=   11          
't value='   tα/2=   1.7959   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   2.9683   / √   12   =   0.856865
margin of error , E=t*SE =   1.7959   *   0.85686   =   1.538830
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    81.58   -   1.539   =   80.044503
Interval Upper Limit = x̅ + E =    81.58   -   1.539   =   83.122164
90%   confidence interval is (   80.04   < µ <   83.12   )

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