SOLUTION: We make the claim that the mean test score on a statistics exam is 75 with σ = 5. We believe the mean may be higher. With 95% confidence, we take a random sample of 25 test

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Question 953982: We make the claim that the mean test score on a statistics exam is 75 with σ = 5. We believe the mean may be higher. With 95% confidence, we take a random sample of 25 test scores to test our theory. (15 Points)
State the null and alternative hypotheses:
Draw the curves and label alpha and beta:
Unstandardize and solve for n:
Answer by stanbon(75887) About Me  (Show Source):
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We make the claim that the mean test score on a statistics exam is 75 with σ = 5. We believe the mean may be higher. With 95% confidence, we take a random sample of 25 test scores to test our theory. (15 Points)
State the null and alternative hypotheses:
Ho: u <= 75
Ha: u > 75 (claim)
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Draw the curves and label alpha and beta:
Draw a normal curve with mean = 0
alpha is 5% and is the right tail of the curve
The remainder of the area under the curve is Beta
The t-score-boundary for the alpha region is t = 1.7109
Unstandardize and solve for n:
The score associated with the boundary = 1.7109(5/sqrt(25))+ 75 = 76.7109
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Cheers,
Stan H.
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