QUESTION: 1069

Which of the is/are false?

A high p-value is necessary to reject a null hypothesis.
II The higher the significance level, the greater is the chance that the null will be rejected when it is false.
III. The higher the probability of Type II error, the higher is the chance of rejecting the null when it is false.
II & III
I, II & III
I only
II only
III only
I & II

Answer(s): B

Explanation:

You can think of the p-value as the maximum probability that the null hypothesis is true despite observing the value of the test statistic that you have in the sample at hand. Thus, the lower the p- value, the greater is your confidence in rejecting the null hypothesis. The significance level represents an upper bound on the probability that the null hypothesis is true given the observed sample and the testing procedure. Hence, if you reject the null at the 5% significance level, for e.g., then the probability that the null is true despite your statistical evidence to the contrary could be as high as 5% (but no more, under the assumptions of the test). A Type II error refers to the event that we will fail to reject the null when it is false. The higher the probability of a Type II error, the lower the chance of rejecting the null when it is false.

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QUESTION: 1070

Mr. and Mrs. Jones live in a neighborhood where the mean family income is $45,000 with a standard deviation of $9,000. Mr. and Mrs. Smith live in a neighborhood where the mean is $100,000 and the standard deviation is $30,000. What is the relative dispersion of the family incomes in the two neighborhoods?

Jones 20%, Smith 30%
Jones 50%, Smith 33%
None of these answers
Jones 40%, Smith 20%
Jones 30%, Smith 20%

Answer(s): A

Explanation:

The coefficient of variation = (s*100)/mean. Jones: 9000*100/45,000 = 20%. Smith: 30,000*100/100,000 = 30% .

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QUESTION: 1071

You have a portfolio of two assets, X and Y. The returns of X and Y follow a joint probability function as follows:
There is a 25% chance that X will return 16% and Y will return 10%; there is a 60% chance that X will return 9% and Y will return 7%; and there is a 15% chance that Y will return 15% and X will return 5%. Find the covariance of X and Y.

3.46%%
1.79%%
-3.46%%
-1.79%%

Answer(s): D

Explanation:

For a joint probability function, the covariance of X and Y is given by the formula: double summation (over all X, and over all Y) of P(X,Y)*[X - E(X)]*[Y - E(Y)]. E(X) will be 25% * 16% + 60% * 9% + 15% * 5% = 4% + 5.4% + 0.75% = 10.15%. Similarly, we will find that E(Y) = 8.95%. Next, we plug these values into our formula and obtain 25% * (16% - 10.15%) *(10% - 8.95%) + 60% (9% - 10.15%) * (7% - 8.95%) + 15% (5% - 10.15%) * (15% - 8.95%) = -1.79%%.

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QUESTION: 1072

Which is true of positively skewed distributions?

They are not symmetrical.
II. Their mean is larger than their median.
III. They are characterized by many small values and a few extreme values.
I and II
I and III
None of these answers is correct.
II and III

Answer(s): C

Explanation:

All are true of positively skewed distributions, so the answer is I, II, and III: None of the above is the correct choice.

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