Question 26

Which of the following statements about testing a hypothesis using a Z-test is least accurate?

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

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

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

D)   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.

Question 27

The average amount of snow that falls during January in Frostbite
    Falls is normally distributed with a mean of 35 inches and a standard deviation of 5 inches. The probability that the snowfall amount in January of next year will be between 40 inches and 26.75 inches is closest to:

A)    68%.

B)   79%.

C)   95%.

D)   87%.

Question 28

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       rejecting a true null hypothesis
B)   Type II error       rejecting a true null hypothesis

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

D)   Type II error       failing to reject a true null hypothesis

Question 29

The possible outcomes for a random variable are described by a continuous uniform distribution with a lower limit of -15 and an upper limit of +25. The probability that the variable has a negative value is closest to:

A)    0.0%.

B)   25.5%.

C)   37.5%.

D)   60.0%.

Question 30

The mean return for the population of all stocks on an exchange in the year 20X1 was 5.0%. The mean return from a sample of 20 randomly selected stocks on that exchange in 20X1 was 4.0%. The difference of -1.0% is best defined as the:

A)    1% confidence interval.

B)   mean sampling difference.

C)   sampling error.

D)   standard error of the sample mean.

[此贴子已经被作者于2008-11-8 18:03:13编辑过]

Question 26

Which of the following statements about testing a hypothesis using a Z-test is least accurate?

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

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

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

D)   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.

The correct answer was B)

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

The significance level is chosen before the test so the calculated Z-statistic can be compared to an appropriate critical value.

This question tested from Session 3, Reading 11, LOS a, (Part 1)

Question 27

The average amount of snow that falls during January in Frostbite Falls is normally distributed with a mean of 35 inches and a standard deviation of 5 inches. The probability that the snowfall amount in January of next year will be between 40 inches and 26.75 inches is closest to:

A)    68%.

B)   79%.

C)   95%.

D)   87%.

The correct answer was B) 79%.

To calculate this answer, we will use the properties of the standard normal distribution. First, we will calculate the Z-value for the upper and lower points and then we will determine the approximate probability covering that range.  Note: This question is an example of why it is important to memorize the general properties of the normal distribution.

Z = (observation – population mean) / standard deviation

• Z_26.75 = (26.75 – 35) / 5 = -1.65. (1.65 standard deviations to the left of the mean)

• Z₄₀ = (40 – 35) / 5 = 1.0 (1 standard deviation to the right of the mean)

Using the general approximations of the normal distribution:

• 68% of the observations fall within ± one standard deviation of the mean. So, 34% of the area falls between 0 and +1 standard deviation from the mean.

• 90% of the observations fall within ± 1.65 standard deviations of the mean. So, 45% of the area falls between 0 and +1.65 standard deviations from the mean.

Here, we have 34% to the right of the mean and 45% to the left of the mean, for a total of 79%.

This question tested from Session 3, Reading 9, LOS h, (Part 2)

Question 28

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       rejecting a true null hypothesis
B)   Type II error       rejecting a true null hypothesis

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

D)   Type II error       failing to reject a true null hypothesis

The correct answer was A) Type I error         rejecting a true null hypothesis

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

This question tested from Session 3, Reading 11, LOS b, (Part 2)

Question 29

The possible outcomes for a random variable are described by a continuous uniform distribution with a lower limit of -15 and an upper limit of +25. The probability that the variable has a negative value is closest to:

A)    0.0%.

B)   25.5%.

C)   37.5%.

D)   60.0%.

The correct answer was C)

In a continuous uniform distribution with a range from a to b, the probability of an outcome within a smaller range of values is equal to the proportion of that range to b – a.

This question tested from Session 3, Reading 9, LOS e

Question 30

The mean return for the population of all stocks on an exchange in the year 20X1 was 5.0%. The mean return from a sample of 20 randomly selected stocks on that exchange in 20X1 was 4.0%. The difference of -1.0% is best defined as the:

A)    1% confidence interval.

B)   mean sampling difference.

C)   sampling error.

D)   standard error of the sample mean.

The correct answer was C)

sampling error.

Sampling error is the difference between a sample statistic and its corresponding population parameter. A confidence interval is a range of estimated values within which the actual value of the parameter will lie with a given probability of 1 - α. The standard error of the sample mean is the standard deviation of the distribution of the sample means.

This question tested from Session 3, Reading 10, LOS a

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