Question 548888: You are given a sample of 106 body temperatures with a mean of 98.20 degrees F. Assume that sigma is known to be 0.62 degrees F. Use a 0.05 significance level to test the claim that the mean body temperature of the population is equal to 98.6 degrees F, as is commonly believed. Is there sufficient evidence to conclude that the common belief is wrong?
Am I supposed to use the null hypothesis to figure this out?
What formula am I supposed to use to get the answer?
How do I interpret the results?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! You are given a sample of 106 body temperatures with a mean of 98.20 degrees F. Assume that sigma is known to be 0.62 degrees F. Use a 0.05 significance level to test the claim that the mean body temperature of the population is equal to 98.6 degrees F, as is commonly believed. Is there sufficient evidence to conclude that the common belief is wrong?
Am I supposed to use the null hypothesis to figure this out?
What formula am I supposed to use to get the answer?
How do I interpret the results?
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Ho: u = 98.6 (claim)
Ha: u # 98.6
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x-bar = 98.2
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t(98.2) = (98.2-98.6)/[0.62/sqrt(106)] = -6.6423
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p(value) = 2*P(z < -6.6423) = 2*tcdf(-100,-6.6423,105) = 0.00000000140
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Since the p-value is less that 1%, reject Ho.
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Conslusion: The test results do not support the claim.
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Cheers,
Stan H.
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