Question 1143854: A data set includes 107 body temperatures of healthy adult humans having a mean of 98.7degreesF and a standard deviation of 0.72degreesF. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6degreesF as the mean body temperature?
What is the confidence interval estimate of the population mean mu?
What does this suggest about the use of 98.6degreesF as the mean body temperature?
A.
This suggests that the mean body temperature could be higher than 98.6degreesF.
B.
This suggests that the mean body temperature could be lower than 98.6degreesF.
C.
This suggests that the mean body temperature could very possibly be 98.6degreesF.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! The sample size of 107 is > 30, so we can use the Normal Distribution probability derived from the z-score tables.
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The sample mean is 98.7 degrees F and the sample standard deviation is 0.72 degrees F
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alpha(a) = 1 - 0.99 = 0.01
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critical probability(p*) = 1 - a/2 = 0.995
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the critical value(cv) is the z-score associated with p*, cv = 2.57
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margin of error(me) = cv * standard deviation = 2.57 * 0.72 = 1.85
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99% confidence interval is 98.7 + or - 1.85, (96.85, 100.55)
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Using the same sampling method, we select different samples of size 107 and compute a different interval estimate for each sample. Some interval estimates would include the true population mean and some would not. A 99% confidence level means that we would expect 99% of the interval estimates to include the population mean.
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answer is C.
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