Question 466980: The Roman Senate has become concerned about the loyalty of the army in Gaul commanded by Julius Caesar. They claim that, of the 80,000 men in the army, at least 28,000 are foreign barbarians. Caesar believes there are fewer barbarians, so the Senate should not worry. He polls one legion of 1,000 men and finds that 340 of them are barbarians. What is the test statistic for this hypothesis test?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The Roman Senate has become concerned about the loyalty of the army in Gaul commanded by Julius Caesar. They claim that, of the 80,000 men in the army, at least 28,000 are foreign barbarians.
Note: Senate claim p = 28/80 = 0.35 barbarians
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Caesar believes there are fewer barbarians, so the Senate should not worry. He polls one legion of 1,000 men and finds that 340 of them are barbarians.
Note: Caesar finds 340/1000 = 0.34 are barbarians
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What is the test statistic for this hypothesis test?
Ho: p >= 0.35 (Senate's claim)
Ha: P < 0.35 Caesar's claim)
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z(0.34) = (0.34-0.35)/sqrt(0.35*0.65/1000) = -0.6630
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P-value = P(z < -0.6630) = 0.2537
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Conclusion: Since the p-value is greater than 5%
fail to reject Ho at the 5% significance level.
Test results support the Senate's claim.
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Cheers,
Stan H
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