What is normal, when it comes to people's body temperatures? A random sample of 130 human body temperatures had a mean of 98.15° and a standard deviation of 0.74°. Does the data indicate that the average body temperature for healthy humans deviates from 98.6°, the usual average temperature cited by physicians and others? (a)
Test using the p-value approach with = 0.05.
State the null and alternative hypothesis.
H0: < 98.6 versus Ha: > 98.6
H0: = 98.6 versus Ha: > 98.6
H0: = 98.6 versus Ha: < 98.6
H0: = 98.6 versus Ha: ≠ 98.6
H0: ≠ 98.6 versus Ha: = 98.6
Find the test statistic and the p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.)
z =
p-value =
State your conclusion.
- The p-value is greater than alpha so H0 is not rejected. There is insufficient evidence to indicate that the average body temperature for healthy humans deviates from 98.6°.
- The p-value is less than alpha so H0 is rejected. There is sufficient evidence to indicate that the average body temperature for healthy humans deviates from 98.6°.
- The p-value is less than alpha so H0 is rejected. There is insufficient evidence to indicate that the average body temperature for healthy humans deviates from 98.6°.
- The p-value is greater than alpha so H0 is not rejected. There is sufficient evidence to indicate that the average body temperature for healthy humans deviates from 98.6°.

(b)
Test using the critical value approach with = 0.05.
Find the rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)
z >
z <
State your conclusion.
- The test statistic does not lie in the rejection region so H0 is not rejected. There is insufficient evidence to indicate that the average body temperature for healthy humans deviates from 98.6°.
- The test statistic lies in the rejection region so H0 is rejected. There is sufficient evidence to indicate that the average body temperature for healthy humans deviates from 98.6°.
- The test statistic lies in the rejection region so H0 is rejected. There is insufficient evidence to indicate that the average body temperature for healthy humans deviates from 98.6°.
- The test statistic does not lie in the rejection region so H0 is not rejected. There is sufficient evidence to indicate that the average body temperature for healthy humans deviates from 98.6°.

(c)
Compare the conclusions from parts (a) and (b). Are they the same?
- Yes, both methods produce the same conclusion.
- No, the p-value approach rejects the null hypothesis when the critical approach fails to reject the null hypothesis.
- No, the critical value approach rejects the null hypothesis when the p-value approach fails to reject the null hypothesis.

(d)
The 98.6° standard was derived by a German doctor in 1868, who claimed to have recorded 1 million temperatures in the course of his research.† What conclusions can you draw about his research in light of your conclusions in parts (a) and (b)?
- It appears as though the the doctor's equipment may not have been accurate.
- It appears as though the doctor was correct in his conclusion.