Q1. A goal of an “innocent until proven guilty” justice system is to place a higher priority on:

A)   avoiding type I errors.

B)   avoiding type II errors.

C)   the null hypothesis.

Q2. If the null hypothesis is innocence, then the statement “It is better that the guilty go free, than the innocent are punished” is an example of preferring a:

A)   type II error over a type I error.

B)   higher level of significance.

C)   type I error over a type II error.

Q3. A bottler of iced tea wishes to ensure that an average of 16 ounces of tea is in each bottle. In order to analyze the accuracy of the bottling process, a random sample of 150 bottles is taken.  Using a t-distributed test statistic of -1.09 and a 5% level of significance, the bottler should:

A)   not reject the null hypothesis and conclude that bottles contain an average 16 ounces of tea.

B)   not reject the null hypothesis and conclude that bottles do not contain an average of 16 ounces of tea.

C)   reject the null hypothesis and conclude that bottles contain an average 16 ounces of tea.

Q4. The power of the test is:

A)     the probability of rejecting a true null hypothesis.

B)     equal to the level of confidence.

C)     the probability of rejecting a false null hypothesis.

Q5. For a t-distributed test statistic with 30 degrees of freedom, a one-tailed test specifying the parameter greater than some value and a 95% confidence level, the critical value is:

A)   1.640.

B)   1.697.

C)   2.042.

答案和详解如下：

Q1. A goal of an “innocent until proven guilty” justice system is to place a higher priority on:

A)   avoiding type I errors.

B)   avoiding type II errors.

C)   the null hypothesis.

Correct answer is A)

In an “innocent until proven guilty” justice system, the null hypothesis is that the accused is innocent. The hypothesis can only be rejected by evidence proving guilt beyond a reasonable doubt, favoring the avoidance of type I errors.

Q2. If the null hypothesis is innocence, then the statement “It is better that the guilty go free, than the innocent are punished” is an example of preferring a:

A)   type II error over a type I error.

B)   higher level of significance.

C)   type I error over a type II error.

Correct answer is A)

The statement shows a preference for accepting the null hypothesis when it is false (a type II error), over rejecting it when it is true (a type I error).

Q3. A bottler of iced tea wishes to ensure that an average of 16 ounces of tea is in each bottle. In order to analyze the accuracy of the bottling process, a random sample of 150 bottles is taken.  Using a t-distributed test statistic of -1.09 and a 5% level of significance, the bottler should:

A)   not reject the null hypothesis and conclude that bottles contain an average 16 ounces of tea.

B)   not reject the null hypothesis and conclude that bottles do not contain an average of 16 ounces of tea.

C)   reject the null hypothesis and conclude that bottles contain an average 16 ounces of tea.

Correct answer is A)

H_o: µ = 16; H_a: µ ≠ 16. Do not reject the null since |t| = 1.09 < 1.96 (critical value).

Q4. The power of the test is:

A)     the probability of rejecting a true null hypothesis.

B)     equal to the level of confidence.

C)     the probability of rejecting a false null hypothesis.

Correct answer is C)

This is the definition of the power of the test: the probability of correctly rejecting the null hypothesis (rejecting the null hypothesis when it is false).

Q5. For a t-distributed test statistic with 30 degrees of freedom, a one-tailed test specifying the parameter greater than some value and a 95% confidence level, the critical value is:

A)   1.640.

B)   1.697.

C)   2.042.

Correct answer is B)

This is the critical value for a one-tailed probability of 5% and 30 degrees of freedom.

谢谢了哈

Q1. The covariance:

A)   must be between -1 and +1.

B)   can be positive or negative.

C)   must be positive.

Correct answer is B)         

Cov(a,b) = σ_aσ_bρ_a,b. Since ρ_a,b can be positive or negative, Cov(a,b) can be positive or negative.

Q2. With respect to the units each is measured in, which of the following is the most easily directly applicable measure of dispersion? The:

A)    covariance.

B)    variance.

C)    standard deviation.

Correct answer is C)

The standard deviation is in the units of the random variable itself and not squared units like the variance. The covariance would be measured in the product of two units of measure.

Q3. Personal Advisers, Inc., has determined four possible economic scenarios and has projected the portfolio returns for two portfolios for their client under each scenario. Personal’s economist has estimated the probability of each scenario as shown in the table below. Given this information, what is the covariance of the returns on Portfolio A and Portfolio B?

A)   0.890223.

B)   0.002019.

C)   0.001898.

Correct answer is C)

Q4. Given Cov(X,Y) = 1,000,000. What does this indicate about the relationship between X and Y?

A)  It is strong and positive.

B)  It is weak and positive.

C)  Only that it is positive.

Correct answer is C)

A positive covariance indicates a positive linear relationship but nothing else. The magnitude of the covariance by itself is not informative with respect to the strength of the relationship.

Q5. Which of the following statements is least accurate regarding covariance?

A)   Covariance can only apply to two variables at a time.

B)   Covariance can exceed one.

C)   A covariance of zero rules out any relationship.

Correct answer is C)

A covariance only measures the linear relationship. The covariance can be zero while a non-linear relationship exists. Both remaining statements are true.

thank you!