JonnyKay

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) significance level of the test is 5%.

C) power of the test is 95%.

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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.

JonnyKay

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) 1.78.

C) 19.06.

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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 / n1/2) = (65,000 – 57,000) / (4,500 / 1151/2) = (8,000) / (4,500 / 10.72) = 19.06.

JonnyKay

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.

JonnyKay

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 / n1/2) = (57,000 – 54,000) / (1,300 / 751/2) = (3,000) / (1,300 / 8.66) = 19.99.

JonnyKay

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 / n1/2) = (67,000 – 58,500) / (5,200 / 1751/2) = (8,500) / (5,200 / 13.22) = 21.62.

JonnyKay

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 / n1/2) = (64,000 – 59,000) / (5,500 / 1351/2) = (5,000) / (5,500 / 11.62) = 10.56.

JonnyKay

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

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

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

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.

JonnyKay

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.

JonnyKay

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

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

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

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.

JonnyKay

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.