Reading 11: Hypothesis Testing-LOS b 习题精选 involving, interpret, hypothesis, 2011

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

LOS b: Define and interpret a test statistic, a Type I and a Type II error, and a significance level, and explain how significance levels are used in hypothesis testing.

 

 

For a two-tailed test of hypothesis involving a z-distributed test statistic and a 5% level of significance, a calculated z-statistic of 1.5 indicates that:

A) the null hypothesis cannot be rejected.

B) the null hypothesis is rejected.

C) the test is inconclusive.

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For a two-tailed test at a 5% level of significance the calculated z-statistic would have to be greater than the critical z value of 1.96 for the null hypothesis to be rejected.

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A pitching machine is calibrated to deliver a fastball at a speed of 98 miles per hour. Every day, a technician samples the speed of twenty-five fastballs in order to determine if the machine needs adjustment. Today, the sample showed a mean speed of 99 miles per hour with a standard deviation of 1.75 miles per hour. Assume the population is normally distributed. At a 95% confidence level, what is the t-value in relation to the critical value?

A) The critical value exceeds the t-value by 1.3 standard deviations.

B) The t-value exceeds the critical value by 0.8 standard deviations.

C) The t-value exceeds the critical value by 1.5 standard deviations.

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t = (99 – 98) / (1.75 / √25) = 2.86. The critical value for a two-tailed test at the 95% confidence level with 24 degrees of freedom is ±2.06 standard deviations. Therefore, the t-value exceeds the critical value by 0.8 standard deviations.

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Kyra Mosby, M.D., has a patient who is complaining of severe abdominal pain. Based on an examination and the results from laboratory tests, Mosby states the following diagnosis hypothesis: H_o: Appendicitis, H_A: Not Appendicitis. Dr. Mosby removes the patient’s appendix and the patient still complains of pain. Subsequent tests show that the gall bladder was causing the problem. By taking out the patient’s appendix, Dr. Mosby:

A) made a Type II error.

B) is correct.

C) made a Type I error.

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This statement is an example of a Type II error, which occurs when you fail to reject a hypothesis when it is actually false (also known as the power of the test).

The other statements are incorrect. A Type I error is the rejection of a hypothesis when it is actually true (also known as the significance level of the test).

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Which of the following statements about hypothesis testing is least accurate?

A) The null hypothesis is a statement about the value of a population parameter.

B) A Type II error is failing to reject a false null hypothesis.

C) If the alternative hypothesis is Ha: μ > μ0, a two-tailed test is appropriate.

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The hypotheses are always stated in terms of a population parameter. Type I and Type II are the two types of errors you can make – reject a null hypothesis that is true or fail to reject a null hypothesis that is false. The alternative may be one-sided (in which case a > or < sign is used) or two-sided (in which case a ≠ is used).

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Which of the following statements about hypothesis testing is most accurate? A Type I error is the probability of:

A) failing to reject a false hypothesis.

B) rejecting a true alternative hypothesis.

C) rejecting a true null hypothesis.

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The Type I error is the error of rejecting the null hypothesis when, in fact, the null is true.

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Which of the following statements about hypothesis testing is least accurate?

A) A Type I error is the probability of rejecting the null hypothesis when the null hypothesis is false.

B) The significance level is the probability of making a Type I error.

C) A Type II error is the probability of failing to reject a null hypothesis that is not true.

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A Type I error is the probability of rejecting the null hypothesis when the null hypothesis is true.

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John Jenkins, CFA, is performing a study on the behavior of the mean P/E ratio for a sample of small-cap companies. Which of the following statements is most accurate?

A) One minus the confidence level of the test represents the probability of making a Type II error.

B) The significance level of the test represents the probability of making a Type I error.

C) A Type I error represents the failure to reject the null hypothesis when it is, in truth, false.

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A Type I error is the rejection of the null when the null is actually true. The significance level of the test (alpha) (which is one minus the confidence level) is the probability of making a Type I error. A Type II error is the failure to reject the null when it is actually false.

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A Type II error:

A) fails to reject a true null hypothesis.

B) rejects a true null hypothesis.

C) fails to reject a false null hypothesis.

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A Type II error is defined as accepting the null hypothesis when it is actually false. The chance of making a Type II error is called beta risk.

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If we fail to reject the null hypothesis when it is false, what type of error has occured?

A) Type II.

B) Type III.

C) Type I.

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A Type II error is defined as failing to reject the null hypothesis when it is actually false.

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Which of the following statements regarding hypothesis testing is least accurate?

A) A type I error is acceptance of a hypothesis that is actually false.

B) The significance level is the risk of making a type I error.

C) A type II error is the acceptance of a hypothesis that is actually false.

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A type I error is the rejection of a hypothesis that is actually true.