Question 1081225
 𝐻0: 𝜇 = 40
&#119867;1: &#120583; < 40
[11.53] The significance level is 5%, the population standard deviation is 5, and the sample size is 25. 
a. Calculate the probability of a Type II error for the above hypotheses when &#120583; = 37
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You have a left-tail test with critical value -1.645
Find the sample mean::
x-bar = 37 - 1.645*5/sqrt(25) = 35.355
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Find the z-score of x-bar:
z(35.355) = (35.355-37)*5/sqrt(25) = -1.645
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Find the P(z > -1645) = 0.99
That is the Probability of a Type II Error
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b. Repeat part a) with &#120572; = 15%
P(Type II Error) = 0.85
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c. Describe the effect on &#120573; of increasing &#120572; 
Since alpha + Beta = 100%, if alpha increases, Beta decreases.
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Cheers,
Stan H.
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