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

A survey is taken to determine whether the average starting salaries of CFA charterholders is equal to or greater than $59,000 per year. What is the test statistic given a sample of 135 newly acquired CFA charterholders with a mean starting salary of $64,000 and a standard deviation of $5,500?

A) 10.56.

B) -10.56.

C) 0.91.

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With a large sample size (135) 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) = (64,000 – 59,000) / (5,500 / 135^1/2) = (5,000) / (5,500 / 11.62) = 10.56.

1215

A survey is taken to determine whether the average starting salaries of CFA charterholders is equal to or greater than $58,500 per year. What is the test statistic given a sample of 175 newly acquired CFA charterholders with a mean starting salary of $67,000 and a standard deviation of $5,200?

A) -1.63.

B) 21.62.

C) 1.63.

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With a large sample size (175) 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) = (67,000 – 58,500) / (5,200 / 175^1/2) = (8,500) / (5,200 / 13.22) = 21.62.

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

Identify the error type associated with the level of significance and the meaning of a 5 percent significance level.

Error type

α = 0.05 means there is a 5 percent probability of

A) Type I error   failing to reject a true null hypothesis

B) Type II error    rejecting a true null hypothesis

C) Type I error    rejecting a true null hypothesis

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The significance level is the risk of making a Type 1 error and rejecting the null hypothesis when it is true.

1215

A survey is taken to determine whether the average starting salaries of CFA charterholders is equal to or greater than $57,000 per year. Assuming a normal distribution, what is the test statistic given a sample of 115 newly acquired CFA charterholders with a mean starting salary of $65,000 and a standard deviation of $4,500?

A) 19.06.

B) -19.06.

C) 1.78.

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With a large sample size (115) 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) = (65,000 – 57,000) / (4,500 / 115^1/2) = (8,000) / (4,500 / 10.72) = 19.06.

1215

If a two-tailed hypothesis test has a 5% probability of rejecting the null hypothesis when the null is true, it is most likely that the:

A) probability of a Type I error is 2.5%.

B) power of the test is 95%.

C) significance level of the test is 5%.

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Rejecting the null hypothesis when it is true is a Type I error. The probability of a Type I error is the significance level of the test. The power of a test is one minus the probability of a Type II error, which cannot be calculated from the information given.

1215

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

A) rejecting a true alternative hypothesis.

B) failing to reject a false null hypothesis.

C) rejecting a true null hypothesis.

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The Type II error is the error of failing to reject a null hypothesis that is not true.

1215

If the probability of a Type I error decreases, then the probability of:

A) a Type II error increases.

B) incorrectly accepting the null decreases.

C) incorrectly rejecting the null increases.

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If P(Type I error) decreases, then P(Type II error) increases. A null hypothesis is never accepted. We can only fail to reject the null.