Q. Suppose we take a random sample of 30 companies in an industry with 200 companies. We calculate the sample mean of the ratio of cash flow to total debt for the prior year. We find that this ratio is 23%. Subsequently, we learn that the population cash flow to total debt ratio (taking account of all 200 companies) is 26%. What is the explanation for the discrepancy between the sample mean of 23% and the population mean of 26%?

• A. Sampling error.
• B. Bias.
• C. A lack of consistency.

A normally distributed random variable has a mean of 100 and a standard deviation of 12. The probability of observing a value greater than 82 is the cumulative distribution function (cdf) of the standard normal variable:

• A. N(1.5).
• B. N(−1.5).
• C. 1 − N(1.5).

None

• A. 6.90%.
• B. 7.14%.
• C. 8.95%.

None

• A. 0.20.
• B. 0.35.
• C. 0.85.

To test whether a particular portfolio’s volatility has changed following the global financial crisis of 2008, an analyst must compare the portfolio’s mean monthly returns and the variances of returns of the pre- and post-crisis periods. The most appropriate test is the:

• A. chi-square test.
• B. F-test.
• C. t-statistic.

None

• A. Fund PQR if the measure of dispersion is the range.
• B. Fund XYZ if the measure of dispersion is the variance.
• C. Fund ABC if the measure of dispersion is the mean absolute deviation.

Q. For a two-sided confidence interval, an increase in the degree of confidence will result in:

• A. a wider confidence interval.
• B. a narrower confidence interval.
• C. no change in the width of the confidence interval.

None

• A. 13.18.
• B. 11.92.
• C. 12.50.

Q. For a binomial random variable with five trials and a probability of success on each trial of 0.50, the distribution will be:

• A. skewed.
• B. uniform.
• C. symmetric.

Q. For a small sample from a normally distributed population with unknown variance, the most appropriate test statistic for the mean is the:

• A. z-statistic.
• B. t-statistic.
• C. χ2 statistic.