High School

**Question 1 (10 points)**

Is normal body temperature the same for men and women? Medical researchers interested in this question collected data from a large number of men and women. Random samples from that data are recorded in the table below.

**Body Temperature (°F)**

- **Female**
97.8
98.0
98.2
98.2
98.6
98.8
98.8
99.2
99.4

- **Male**
96.9
97.4
97.8
97.8
97.9
98.0
98.1
98.6
98.8

Two random samples of body temperatures.
[Source: Journal of Statistics Education Data Archive, www.amstat.org, April 15, 2002.]

a) Use a 95% confidence interval to estimate the mean body temperature of men.
b) Use a 95% confidence interval to estimate the mean body temperature of women.
c) Find the margin of error for the men and for the women.
d) Which margin of error is larger? Why is it larger?

Answer :

a. The mean body temperature of men is roughly 97.5°F to 98.3°F.

b. The 95% confidence interval is approximately 98.3°F to 99.1°F.

c. The margin of error for men is about 0.4°F and for women is roughly 0.4°F,

d. The margin of error for women is larger due to a wider range of recorded temperatures in the sample

How to solve

a) The mean body temperature for men in this sample is 97.9°F.

Using a t-distribution (as we don't know the population standard deviation), the 95% confidence interval for the mean body temperature of men is roughly 97.5°F to 98.3°F.

b) For women, the mean is 98.7°F. The 95% confidence interval is approximately 98.3°F to 99.1°F.

c) The margin of error for men is about 0.4°F and for women is roughly 0.4°F, assuming equal sample sizes and degrees of freedom.

d) The margin of error for women is larger due to a wider range of recorded temperatures in the sample, which increases variability and uncertainty in the estimate.

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