Reading 11: Hypothesis Testing LOS a习题精选 2010, describe, interpret, hypothesis

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

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

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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In order to test whether the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the sample value of the computed test statistic, t_n-1 = 3.4. The null and alternative hypotheses are:

A) H0: μ = 100; Ha: μ ≠ 100.

B) H0: μ ≤ 100; Ha: μ > 100.

C) H0: X ≤ 100; Ha: X > 100.

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The null hypothesis is that the theoretical mean is not significantly different from zero. The alternative hypothesis is that the theoretical mean is greater than zero.

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In a two-tailed test of a hypothesis concerning whether a population mean is zero, Jack Olson computes a t-statistic of 2.7 based on a sample of 20 observations where the distribution is normal. If a 5% significance level is chosen, Olson should:

A) reject the null hypothesis and conclude that the population mean is not significantly different from zero.

B) fail to reject the null hypothesis that the population mean is not significantly different from zero.

C) reject the null hypothesis and conclude that the population mean is significantly different from zero.

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At a 5% significance level, the critical t-statistic using the Student’s t-distribution table for a two-tailed test and 19 degrees of freedom (sample size of 20 less 1) is ± 2.093 (with a large sample size the critical z-statistic of 1.960 may be used). Because the critical t-statistic of 2.093 is to the left of the calculated t-statistic of 2.7, meaning that the calculated t-statistic is in the rejection range, we reject the null hypothesis and we conclude that the population mean is significantly different from zero.

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What kind of test is being used for the following hypothesis and what would a z-statistic of 1.68 tell us about a hypothesis with the appropriate test and a level of significance of 5%, respectively?

H₀: B ≤ 0
H_A: B > 0

A) One-tailed test; fail to reject the null.

B) Two-tailed test; fail to reject the null.

C) One-tailed test; reject the null.

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The way the alternative hypothesis is written you are only looking at the right side of the distribution. You are only interested in showing that B is greater than 0. You don't care if it is less than zero. For a one-tailed test at the 5% level of significance, the critical z value is 1.645. Since the test statistic of 1.68 is greater than the critical value we would reject the null hypothesis.

 

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

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Jo Su believes that there should be a negative relation between returns and systematic risk. She intends to collect data on returns and systematic risk to test this theory. What is the appropriate alternative hypothesis?

A) Ha: ρ < 0.

B) Ha: ρ > 0.

C) Ha: ρ ≠ 0.

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The alternative hypothesis is determined by the theory or the belief. The researcher specifies the null as the hypothesis that she wishes to reject (in favor of the alternative). The theory in this case is that the correlation is negative.

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If the null hypothesis is H₀: ρ ≤ 0, what is the appropriate alternative hypothesis?

A) Ha: ρ ≠ 0.

B) Ha: ρ < 0.

C) Ha: ρ > 0.

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The alternative hypothesis must include the possible outcomes the null does not.

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In order to test if the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the sample value of the computed test statistic, t_n-1 = 1.2. If you choose a 5% significance level you should:

A) reject the null hypothesis and conclude that the population mean is greater than 100.

B) fail to reject the null hypothesis and conclude that the population mean is greater than 100.

C) fail to reject the null hypothesis and conclude that the population mean is not greater than 100.

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At a 5% significance level, the critical t-statistic using the Student’s t distribution table for a one-tailed test and 29 degrees of freedom (sample size of 30 less 1) is 1.699 (with a large sample size the critical z-statistic of 1.645 may be used). Because the critical t-statistic is greater than the calculated t-statistic, meaning that the calculated t-statistic is not in the rejection range, we fail to reject the null hypothesis and we conclude that the population mean is not significantly greater than 100.

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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.