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In: Statistics and Probability

4. Suppose that we want to test the null hypothesis that the mean of a normal...

4. Suppose that we want to test the null hypothesis that the mean of a normal population with    σ2 =1. Ho: μ = 10 vs Ha: μ > 10.   Determine the minimum sample size needed to test with β(11) = 0.06.

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From the given data

True mean   µ =    11                              
hypothesis mean,   µo =    10                              
and α =    0.05                              
Variance = 1 => std.dev = 1
beta =       0.06                              
delta = true mean - hypothesis mean = 11 -1 = 10   
Z ( 0.05 ) = 1.6449   [excel function: =normsinv(0.05)                          
  Z (0.06) = 1.5548   [excel function: =normsinv(0.06                       
  sample size formula = n = ( ( Z(ß)+Z(α) )*σ / δ )² =

( (1.5548+ 1.64 ) 1.0 / ) ² =   10.24 ~ 11
                                          

orchestra answered 1 year ago
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