Reading 11: Hypothesis Testing-LOS a 习题精选 2011, hypothesis, interpret, describe

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Session 3: Quantitative Methods: Application
Reading 11: Hypothesis Testing

LOS a: Define a hypothesis, describe the steps of hypothesis testing, interpret and discuss the choice of the null hypothesis and alternative hypothesis, and distinguish between one-tailed and two-tailed tests of hypotheses.

 

 

Which of the following statements about testing a hypothesis using a Z-test is least accurate?

A) The calculated Z-statistic determines the appropriate significance level to use.

B) If the calculated Z-statistic lies outside the critical Z-statistic range, the null hypothesis can be rejected.

C) The confidence interval for a two-tailed test of a population mean at the 5% level of significance is that the sample mean falls between ±1.96 σ/√n of the null hypothesis value.

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The significance level is chosen before the test so the calculated Z-statistic can be compared to an appropriate critical value.

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

A) H0: μ ≤ 0.10 versus Ha: μ > 0.10.

B) H0: μ = 0.10 versus Ha: μ ≠ 0.10.

C) H0: μ ≥ 0.10 versus Ha: μ < 0.10.

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

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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 or equal to for the null and less than for the alternative.

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

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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.

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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) greater than returns on other days.

B) less than returns on other days.

C) not greater than returns on other days.

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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.

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

A) H0: μ ≤ 0.10 versus Ha: μ > 0.10.

B) H0: μ < 0.10 versus Ha: μ > 0.10.

C) H0: μ > 0.10 versus Ha: μ < 0.10.

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This is a one-sided alternative because of the "greater than" belief.

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

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

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

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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.

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

A) hypothesis to be proved through statistical testing.

B) hoped-for outcome.

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

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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.

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

A) H0: μ < 0.15 versus Ha: μ = 0.15.

B) H0: μ ≥ 0.15 versus Ha: μ < 0.15.

C) H0: μ = 0.15 versus Ha: μ ≠ 0.15.

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

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George Appleton believes that the average return on equity in the amusement industry, μ, is greater than 10%. What is the null (H₀) and alternative (H_a) hypothesis for his study?

A) H0: > 0.10 versus Ha: ≤ 0.10.

B) H0: > 0.10 versus Ha: < 0.10.

C) H0: ≤ 0.10 versus Ha: > 0.10.

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The alternative hypothesis is determined by the theory or the belief. The researcher specifies the null as the hypothesis that he wishes to reject (in favor of the alternative). Note that this is a one-sided alternative because of the "greater than" belief.

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A researcher is testing the hypothesis that a population mean is equal to zero. From a sample with 64 observations, the researcher calculates a sample mean of -2.5 and a sample standard deviation of 8.0. At which levels of significance should the researcher reject the hypothesis?

1% significance

5% significance

10% significance

A) Fail to reject Reject Reject

B) Fail to reject Fail to reject Reject

C) Reject Fail to reject Fail to reject

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This is a two-tailed test. With a sample size greater than 30, using a z-test is acceptable. The test statistic = = ?2.5. For a two-tailed z-test, the critical values are ±1.645 for a 10% significance level, ±1.96 for a 5% significance level, and ±2.58 for a 1% significance level. The researcher should reject the hypothesis at the 10% and 5% significance levels, but fail to reject the hypothesis at the 1% significance level.

Using Student's t-distribution, the critical values for 60 degrees of freedom (the closest available in a typical table) are ±1.671 for a 10% significance level, ±2.00 for a 5% significance level, and ±2.66 for a 1% significance level. The researcher should reject the hypothesis at the 10% and 5% significance levels, but fail to reject the hypothesis at the 1% significance level.