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Basic Math

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Consider the following hypothesis test.
H₀: Î¼ = 30
H_a: Î¼ â‰ 30
The population standard deviation is 14.UseÂ Â Î± = 0.05. How large a sample should betaken if the researcher is willing to accept a 0.10 probability ofmaking a type II error when the actual population mean is 34?

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True meanÂ Â Âµ = Â Â 34Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
hypothesis mean,Â Â Âµo = Â Â 30Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
Level of Significance , Â Â Î± = Â Â 0.05Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
std dev = Â Â Ïƒ = Â Â 14Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
ÃŸ=Â Â Â Â Â 0.1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
Î´=Â Â Âµ - Âµo = Â Â 4Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
Z (Î±/2)=Â Â Â Â Â 1.9600Â Â

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