SOLUTION: A local politician running for reelection clains that the mean prison time for car theives is le4ss than the required 6 years. A sample of 80 convicted car theives was randomly sel

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Question 244626: A local politician running for reelection clains that the mean prison time for car theives is le4ss than the required 6 years. A sample of 80 convicted car theives was randomly selected. The mean of the sample was found to be 5.5 years. The population standard deviation is known to be 1.25 years. At a=0.05, test the politicians claim
Answer by stanbon(75887) (Show Source):
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A local politician running for reelection clains that the mean prison time for car theives is le4ss than the required 6 years. A sample of 80 convicted car theives was randomly selected. The mean of the sample was found to be 5.5 years. The population standard deviation is known to be 1.25 years. At a=0.05, test the politicians claim
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Ho: u >= 6
H1: u < 6
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Critical Value for left tail test with
alpha = 5% and df = 79 ; t = -1.6664..
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Test statistic: t(5.5) = (5.5-6)/[1.25/sqrt(80)]
= -3.578
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Conclusion: Since the ts is in the reject interval
reject Ho and accept the claim.
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Cheers,
Stan H.