1.Given a mean of 10 percent and a standard error of 14 percent, what is a 95 percent

A)   -17.44% to 37.44%.

B)   -4.00% to 24.00%.

C)   -17.00% to 38.00%.

D)   -12.56% to 25.44%.

2.Ryan McKeeler and Howard Hu, two junior statisticians, were discussing the relation between confidence intervals and hypothesis tests. During their discussion each of them made the following statement:

McKeeler: A confidence interval for a two-tailed hypothesis test is calculated as adding and subtracting the product of the standard error and the critical value from the sample statistic. For example, for a level of confidence of 68 percent, there is a 32 percent probability that the true population parameter is contained in the interval.

Hu: A 99 percent confidence interval uses a critical value associated with a given distribution at the 1 percent level of significance. A hypothesis test would compare a calculated test statistic to that critical value. As such, the confidence interval is the range for the test statistic within which a researcher would not reject the null hypothesis for a two-tailed hypothesis test about the value of the population mean of the random variable.

Are the statements as made by McKeeler and Hu correct?

A)         Incorrect                     Incorrect

B)         Incorrect                     Correct

C)         Correct                       Correct

D)         Correct                       Incorrect

答案和详解如下：

1.Given a mean of 10 percent and a standard error of 14 percent, what is a 95 percent

A)   -17.44% to 37.44%.

B)   -4.00% to 24.00%.

C)   -17.00% to 38.00%.

D)   -12.56% to 25.44%.

confidence interval for the return next year?

The correct answer was A)

10% +/-14(1.96) = -17.44% to 37.44%.

2.Ryan McKeeler and Howard Hu, two junior statisticians, were discussing the relation between confidence intervals and hypothesis tests. During their discussion each of them made the following statement:

McKeeler: A confidence interval for a two-tailed hypothesis test is calculated as adding and subtracting the product of the standard error and the critical value from the sample statistic. For example, for a level of confidence of 68 percent, there is a 32 percent probability that the true population parameter is contained in the interval.

Hu: A 99 percent confidence interval uses a critical value associated with a given distribution at the 1 percent level of significance. A hypothesis test would compare a calculated test statistic to that critical value. As such, the confidence interval is the range for the test statistic within which a researcher would not reject the null hypothesis for a two-tailed hypothesis test about the value of the population mean of the random variable.

Are the statements as made by McKeeler and Hu correct?

McKeeler

Hu

A)         Incorrect                     Incorrect

B)         Incorrect                     Correct

C)         Correct                       Correct

D)         Correct                       Incorrect

The correct answer was B)

McKeeler’s statement is incorrect. Specifically, for a level of confidence of say, 68 percent, there is a 68 percent probability that the true population parameter is contained in the interval. Therefore, there is a 32 percent probability that the true population parameter is not contained in the interval. Hu’s statement is correct.