Carlisle conducted an experiment to determine if the there is a difference in mean body temperature for men and women. He found that the mean body temperature for a sample of 100 men was 97.9 with a population standard deviation of 0.57 and the mean body temperature for a sample of 100 women was 98.6 with a population standard deviation of 0.55.

Assuming the population of body temperatures for men and women is normally distributed, calculate the 99% confidence interval and the margin of error for the mean body temperature for both men and women. Using complete sentences, explain what these confidence intervals mean in the context of the problem.

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Maria:

This looks like a Statistics problem to me, not "Math" as I see classified.
You also must assume that the twosamples of size 100 are random and independent. Note that the population std. dev. are known (given)

for men the 99% confidence interval for the population mean body temperature Is [97.753, 98.047]
for women the 99% confidence interval for the population mean body temperature Is [98.458, 98.742]

The respective margins of error are the differences between the upper and lower limits.

Margin of error for men 0.294
Margin of error for women 0.284

Note that the two confidence intervals DO NOT overlap.

This shows that, under the assumptions stated above, the data provide highly significant (at 1 - 0.99 = 1% level of significance) evidence against the null hypothesis that the mean body temperature of the population of men under consideration is equal to the mean body temperature of the population of women under consideration.

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