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In: Statistics and Probability

Ian is testing to see if Irvinites eat more fruits and vegetables than the average American....

Ian is testing to see if Irvinites eat more fruits and vegetables than the average American. Previous research indicates that Irvinites eat 5.8 servings per day. The national average is 4.6 with a standard deviation of three. How many people does Josh need in his sample to achieve a power of .80

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Expert Solution

True mean,   µ =    5.8                              
hypothesis mean,   µo =    4.6                              
                                      
Level of Significance ,    α =    0.05                              
std dev =    σ =    3
power =    0.8                              
ß= 1-power = 0.2                              
δ=   µ - µo =    1.2                              
                                      
Z ( α ) =       1.6449   [excel function: =normsinv(α)                          
                                     
Z (ß) =        0.8416   [excel function: =normsinv(ß)                         
                                      
sample size needed =    n = ( ( Z(ß)+Z(α) )*σ / δ )² = ( (   0.8416   +   1.6449   ) *   3.0   /   1.2   ) ² =   38.6410
                                      
so, sample size =        39   

orchestra answered 11 months ago
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