Question 1081225: 𝐻0: 𝜇 = 40
𝐻1: 𝜇 < 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 𝜇 = 37
b. Repeat part a) with 𝛼 = 15%
c. Describe the effect on 𝛽 of increasing 𝛼
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 𝐻0: 𝜇 = 40
𝐻1: 𝜇 < 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 𝜇 = 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 𝛼 = 15%
P(Type II Error) = 0.85
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c. Describe the effect on 𝛽 of increasing 𝛼
Since alpha + Beta = 100%, if alpha increases, Beta decreases.
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Cheers,
Stan H.
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