QUESTION: 685

Which of the following is/are true?

If a test always rejects the null, its significance level is zero.
II. If a test always accepts the null, the probability of type II error equals zero.
III. If the p-value exceeds the significance level, you cannot reject the null.
II only
I only
III only
II & III

Answer(s): C

Explanation:

The lowest significance level at which the null hypothesis can be rejected is called the p-value of the test. Thus, if the p-value is less than the significance level, the null hypothesis can be rejected at that significance level; otherwise, you must fail to reject the null. The significance level in hypothesis testing refers to the probability that we will reject the null when it is true. Hence, if we always reject the null, the probability of rejecting it when it is true equals 1. A Type II error occurs when we fail to reject the null when in fact it is false. Therefore, if we always accept the null, we will never reject it even when it is false. So the probability of Type II error will equal 1.

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QUESTION: 686

You are given n = 12, sum of the (X_i) = 2%, sum of the (X_i)^2 = 0.5%%. Find the sample standard deviation.

1.27%.
1.73%.
1.23%.
1.11%.

Answer(s): C

Explanation:

The sample standard deviation will be the positive square root of the sample variance. The sample variance will be determined using the computational formula [1/(n-1)] * {sum (as i goes from 1 to n) of (X_i)^2 - (1/n) * [sum (as i goes from 1 to n) of (X_i)]^2}. So we get 1/11 * (0.5 - 1/12*(2^2)) = 1.51%%. The positive square root of 1.51%% is 1.23%.

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QUESTION: 687

Sharleef Nettleton, a quantitative analyst with Churn Brothers Brokerage, is examining a data sample and has amassed the following information:
Standard deviation of the sample: 2.90
Number of observations: 68
Degrees of freedom: 2
Sample mean: 114

Assume that Ms. Nettleton formulates a null hypothesis that states that the value of the population mean is zero. Additionally, assume that the population standard deviation is unknown. Given this information, what is the standard error of the estimate? Further, what is the test statistic? Choose the best answer.

1.0199; 111.78
0.3517; 84.34
1.0199; 56.44
0.3517; 324.14
None of these answers is correct.
0.3570; 29.91
0.3570; 319.38

Answer(s): D

Explanation:

If the population standard deviation is unknown, as in this example, the standard error of the estimate is found by using the following equation:
{Standard error = s / square root of n} where s = the sample standard deviation and n = the number of observations in the sample.
In this example, all of the necessary information has been provided, and the determination of the standard error of the estimate is found as:
{Standard error = [2.90 / 8.2462] = 0.3517}
Now that the standard error of the estimate has been calculated, the test statistic can be found by using the following equation:
{Test statistic = [sample statistic - value of the population parameter under the null hypothesis] / standard error of the sample statistic].
Again, all of the necessary information has been provided, and the calculation of the test statistic is found as follows:
{Test statistic = [114 - 0] / 0.3517 = 324.14}
This is a very large test statistic and the null hypothesis will likely be rejected unless a very low level of confidence is employed.

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QUESTION: 688

If all the 10,000 data points in a regression lie exactly on a straight line, which of the following is/are true?

The intercept term is zero.
II. The percentage of unexplained variance equals zero
III. The slope coefficient is positive.
IV. The correlation coefficient between the dependent and independent variables is 1.
III only
IV only
II & IV
III & IV
II only
I only

Answer(s): E

Explanation:

Since there is no error in the regression, the percentage of unexplained variance will be zero. The intercept and slope terms can be any real numbers and the correlation coefficient will be either + 1 or - 1.

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QUESTION: 685

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QUESTION: 686

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QUESTION: 687

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QUESTION: 688

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