Reading 11: Hypothesis Testing - LOS a, (Part 2) ～ Q1-6

答案和详解如下：

1.Robert Patterson, an options trader, believes that the return on options trading is higher on Mondays than on other days. In order to test his theory, he formulates a null hypothesis. Which of the following would be an appropriate null hypothesis? Returns on Mondays are:

A)   not greater than returns on other days.

B)   greater than returns on other days.

C)   less than returns on other days.

D)   not less than returns on other days.

The correct answer was A)

An appropriate null hypothesis is one that the researcher wants to reject. If Patterson believes that the returns on Mondays are greater than on other days, he would like to reject the hypothesis that the opposite is true–that returns on Mondays are not greater than returns on other days.

2.James Ambercrombie believes that the average return on equity in the utility industry, µ, is greater than 10 percent. What is null (H₀) and alternative (H_a) hypothesis for his study?

A)   H₀: µ ≥ 0.10 versus H_a: µ < 0.10.

B)   H₀: µ ≤ 0.10 versus H_a: µ > 0.10.

C)   H₀: µ = 0.10 versus H_a: µ ≠ 0.10.

D)   H₀: µ ≠ 0.10 versus H_a: µ = 0.10.

The correct answer was B)

This is a one-sided alternative because of the “greater than” belief. We expect to reject the null.

3.Jill Woodall believes that the average return on equity in the retail industry, µ, is less than 15 percent. What is null (H₀) and alternative (H_a) hypothesis for her study?

A)   H₀: µ ≥ 0.15 versus H_a: µ < 0.15.

B)   H₀: µ < 0.15 versus H_a: µ = 0.15.

C)   H₀: µ = 0.15 versus H_a: µ ≠ 0.15.

D)   H₀: µ ≠ 0.15 versus H_a: µ = 0.15.

The correct answer was A)

This is a one-sided alternative because of the “less than” belief. We expect to reject the null.

4.What is the most common formulation of null and alternative hypotheses?

A)   Less than for the null and greater than for the alternative.

B)   Greater than for the null and less than for the alternative.

C)   Equal to for the null and not equal to for the alternative.

D)   Greater than or equal to for the null and less than for the alternative.

The correct answer was C)

The most common set of hypotheses will take the form of an equal to statement for the null and a not equal to statement for the alternative.

5.Which one of the following best characterizes the alternative hypothesis? The alternative hypothesis is usually the:

A)   hypothesis that is proved through statistical testing.

B)   hoped-for outcome.

C)   hypothesis to be proved through statistical testing.

D)   hypothesis that is accepted after a statistical test is conducted.

The correct answer was B)

The alternative hypothesis is typically the hypothesis that a researcher hopes to support after a statistical test is carried out. We can reject or fail to reject the null, not 'prove' a hypothesis.

6.Which one of the following is the most appropriate set of hypotheses to use when a researcher is trying to demonstrate that a return is greater than the risk-free rate? The null hypothesis is framed as a:

A)   greater than statement and the alternative hypothesis is framed as a less than or equal to statement.

B)   less than or equal to statement and the alternative hypothesis is framed as a greater than statement.

C)   less than statement and the alternative hypothesis is framed as a greater than or equal to statement.

D)   greater than or equal to statement and the alternative hypothesis is framed as a less than statement.

The correct answer was B)

If a researcher is trying to show that a return is greater than the risk-free rate then this should be the alternative hypothesis. The null hypothesis would then take the form of a less than or equal to statement.