1215

A survey is taken to determine whether the average starting salaries of CFA charterholders is equal to or greater than $54,000 per year. Assuming a normal distribution, what is the test statistic given a sample of 75 newly acquired CFA charterholders with a mean starting salary of $57,000 and a standard deviation of $1,300?

A) 19.99.

B) 2.31.

C) -19.99.

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With a large sample size (75) the z-statistic is used. The z-statistic is calculated by subtracting the hypothesized parameter from the parameter that has been estimated and dividing the difference by the standard error of the sample statistic. Here, the test statistic = (sample mean – hypothesized mean) / (population standard deviation / (sample size)^1/2 = (X ? μ) / (σ / n^1/2) = (57,000 – 54,000) / (1,300 / 75^1/2) = (3,000) / (1,300 / 8.66) = 19.99.

1215

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.

1215

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.

1215

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.

1215

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.

1215

A Type I error:

A) rejects a false null hypothesis.

B) fails to reject a false null hypothesis.

C) rejects a true null hypothesis.

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A Type I Error is defined as rejecting the null hypothesis when it is actually true. The probability of committing a Type I error is the significance level or alpha risk.

1215

Which of the following statements regarding Type I and Type II errors is most accurate?

A) A Type I error is failing to reject the null hypothesis when it is actually false.

B) A Type I error is rejecting the null hypothesis when it is actually true.

C) A Type II error is rejecting the alternative hypothesis when it is actually true.

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A Type I Error is defined as rejecting the null hypothesis when it is actually true. The probability of committing a Type I error is the risk level or alpha risk.

1215

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).

1215

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).

1215

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.