SOLUTION: A test of sobriety involves measuring the subjects motor skills. Twenty randomly selected sober subjects take the test and produce a mean score of 41.0 with a standard deviation of

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Question 181215This question is from textbook
: A test of sobriety involves measuring the subjects motor skills. Twenty randomly selected sober subjects take the test and produce a mean score of 41.0 with a standard deviation of 3.7. At the 0.01 level of significance, test the claim that the true mean score for all sober subjects is equal to 35.0. You may assume that sobriety is normally distributed. This question is from textbook

Answer by stanbon(75887) About Me  (Show Source):
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A test of sobriety involves measuring the subjects motor skills.
Twenty randomly selected sober subjects take the test and produce a mean score of 41.0 with a standard deviation of 3.7.
At the 0.01 level of significance, test the claim that the true mean score for all sober subjects is equal to 35.0.
You may assume that sobriety is normally distributed.
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Ho: u = 35
Ha: u is not equal to 35
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Two-tail test with alpha = 1% has critical value z = 2.576
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Test statistic: z(41) = (41-35)/[3.7/sqrt(20)] = 7.252
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Conclusion: Since t.s. is in the reject interval, Reject Ho.
The test provides evidence that u is not equal to 35.
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Cheers
Stan H.