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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Answer:

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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