A philosophy professor wants to find out whether the mean age of the men in his large lecture class is equal to the mean age of the women in his classes. After collecting data from a random sample of his students, the professor tested the hypothesis $\mathrm { H } _ { 0 } : \mu _ { M } - \mu _ { W } = 0$ against the alternative $\mathrm { H } _ { \mathrm { A } } : \mu _ { M } -$ $\mu W \neq 0$. The $P$-value for the test was $0.003$. Which is true?
A) There is a 99.7% chance that another sample will give these same results.
B) There is a 0.3% chance that the mean ages for the men and women are different.
C) There is a 0.3% chance that the mean ages for the men and women are equal.
D) It is very unlikely that the professor would see results like these if the mean age of men was equal to the mean age of women.
E) There is a 0.3% chance that another sample will give these same results.

Question

Quizplus · Accepted Answer

The p-value of 0.003 indicates that if the null hypothesis were true (mean ages are equal), there is only a 0.3% chance of observing results as extreme as those obtained. This suggests it is very unlikely to see such results if the mean ages were actually equal.

A Philosophy Professor Wants to Find Out Whether the Mean H0:μM−μW=0\mathrm { H } _ { 0 } : \mu _ { M } - \mu _ { W } = 0H0​:μM​−μW​=0

A Philosophy Professor Wants to Find Out Whether the Mean $\mathrm { H } _ { 0 } : \mu _ { M } - \mu _ { W } = 0$