You wish to test the hypothesis that female college students spend more on wearing apparel than male college students. Which of the following is INCORRECT? A) The null and alternate hypotheses are: H_o : m_F $\le$ m_M H_A : m_F m_M B) If you concluded that female students spend more than male students when in fact there is no difference between the two groups, you would be committing a Type II error. C) The probability of concluding that females spend more than male students when in fact this is the case, is called the power of the test. D) If in testing the above hypothesis, we insist on reducing the probability of making the Type I error, ceteris paribus the probability of Type II error will increase. E) If we conclude that females spend less than males when in fact that is the case, we have made a correct decision.

Question

You wish to test the hypothesis that female college students spend more on wearing apparel than male college students. Which of the following is INCORRECT? A) The null and alternate hypotheses are: H_o : m_F $\le$ m_M H_A : m_F > m_M B) If you concluded that female students spend more than male students when in fact there is no difference between the two groups, you would be committing a Type II error. C) The probability of concluding that females spend more than male students when in fact this is the case, is called the power of the test. D) If in testing the above hypothesis, we insist on reducing the probability of making the Type I error, ceteris paribus the probability of Type II error will increase. E) If we conclude that females spend less than males when in fact that is the case, we have made a correct decision.

Quizplus · Accepted Answer

EB) Committing a Type II error actually means failing to reject the null hypothesis when it is false. In this context, it would mean concluding there is no difference in spending when, in fact, females spend more. The description given matches a Type I error, not Type II.E) The statement is not related to the hypothesis testing being discussed. The hypothesis test is designed to assess whether females spend more than males, not whether they spend less. Concluding females spend less than males is not a decision directly derived from the hypothesis test described.

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