【DOC】-2009年金融风险管理师 frm 基础阶段数量习题

【DOC】-2009年金融风险管理师 frm 基础阶段数量习 2009年金融风险管理师 frm 基础阶段数量习题 Quantitative Methods Question 1 A conditional expectation involves: A. determining the expected joint probability. B. calculating the conditional variance. C. estimating the skewness. D. refining a forecast because of the occurrence of some other event. Question 2 If two fair coins are flipped and two fair six-sided dice are rolled, all at the same time, what is the probability of ending up with two heads (on the coins) and two sixes (on the dice)? A. 0.4167. B. 0.0039. C. 0.8333. D. 0.0069. Question 3 If X and Y are independent random variables: A. the covariance between the two variables is equal to zero. B. the correlation between the two variables is equal to zero. C. The covariance between the two variables is equal to zero and the correlation between the two variables is equal to zero. D. the variables are perfectly correlated. Question 4 For two (possibly dependent) random variables, X and Y, an upper bound on the covariance of X and Y is: A. σ(X) .σ(Y). B. 1. C. there is no upper bound unless the variables are independent. D. zero. Question 5 Tully Advisers, Inc. has determined four possible economic scenarios and has projected the portfolio returns for two portfolios for their client under each scenario. Tully’s economist has estimated the probability of each scenario as shown in the table below. Given this information, what is the expected return on portfolio A? Scenario Probability Return on Portfolio A Return on Portfolio B A B C 15% 20% 25% 17% 14% 12% 19% 18% 10% 1-26 D 40% 8% 9% A. B. C. D. 9.25%. 10.75% 12.95%. 11.55%. Question 6 Bonds rated B have a 25 percent chance of default in five years. Bonds rated CCC have a 40 percent chance of default in five years. A portfolio consists of 30 percent B and 70 percent CCC-rated bonds. If a randomly selected bond defaults in a five-year period, what is the probability that it was a B-rated bond? A. 0.625. B. 0.211. C. 0.429. D. 0.250. Question 7 A portfolio manager wants to eliminate four stocks from a portfolio that consists of six stocks. How many ways can the four stocks be sold when the order of the sales is important? A. 24. B. 360. C. 720. D. 180. Question 8 If the probability of both a new Wal-Mart and a new Wendy’s being built next month is 68 percent and the probability of a new Wal-Mart being built is 85 percent, what is the probability of a new Wendy’s being built if a new Wal-Mart is built? A. 0.80. B. 0.70. C. 0.60. D. 0.85. Question 9 There is an 80 percent chance of rain on each of the next six days. What is the probability that it will rain on exactly two of those days? A. 0.15364. B. 0.24327. C. 0.01536. D. 0.35678. Question 10 Given the following table about employees of a company based on whether they are smokers or nonsmokers and whether or not they suffer from any allergies, what is the probability of both 2-26 suffering from allergies and not suffering from allergies? Suffer from Allergies Smoker 35 Nonsmoker 55 Total 90 Don't Suffer from Allergies 25 185 210 Total 60 240 300 A. B. C. D. 0.50. 1.00. 0.00. 0.24. Question 11 The correlation coefficient for two dependent random variables is equal to: A. the product of the standard deviations for the two random variables divided by the covariance. B. the covariance between the random variables divided by the product of the variances. C. the covariance between the random variables divided by the product of the standard deviations. D. the absolute value of the difference between the means of the two variables divided by the product of the variances. Question 12 The following table summarizes the availability of trucks with air bags and bucket seats at a dealership. Air Bags No Air Bags Total Bucket seats No Bucket SeatsTotal75 35 110 50 60 110 12595 220 What is the probability of randomly selecting a truck with air bags and bucket seats? A. 0.16. B. 0.28. C. 0.34. D. 0.57. Question 13 If a fair coin is tossed twice, what is the probability of obtaining heads both times? A. 1/2. B. 3/4. C. 1. D. 1/4. 3-26 Question 14 A bag contains 3 white and 4 green balls. What is the probability that if 2 balls are drawn at random without replacement, both the balls are white? A. 1/6. B. 1/5. C. 1/7. D. 1/4. Question 15 There is a 30% chance that the economy will be good and a 70% chance that it will be bad. If the economy is good, your returns will be 20% and if the economy is bad, your returns will be 10%. What is your expected return? A. 15%. B. 13%. C. 17%. D. 18%. Question 16 A dealer in a casino has rolled a five on a single die three times in a row. What is the probability of her rolling another five on the next roll, assuming it is a fair die? A. 0.001. B. 0.167. C. 0.500. D. 0.200. Question 17 Use the following probability distribution to calculate the standard deviation for the portfolio. State of the Economy Probability Return on Portfolio Boom 0.30 15% Bust 0.70 3% A. B. C. D. 6.0% 6.5%. 7.0%. 5.5%. Question 18 Which of the following statements about probability is TRUE? A. An event is a set of one or more possible values of a random variable B. A conditional probability is the probability that two or more events will happen concurrently. C. An outcome is the calculated probability of an event. D. Out of a sample of 100 widgets 10 were found to be defective, 20 were perfect, and 70 were OK. The probability of picking a perfect widget at random is 29 percent. 4-26 Question 19 The variance of the sum of two independent random variables is equal to the sum of their variances: A. plus a positive covariance term. B. minus a positive covariance term. C. plus a non-zero covariance term. D. plus zero. Question 20 An investor has an A-rated bond, a BB-rated bond, and a CCC-rated bond where the probabilities of default over the next three years are 4 percent, 12 percent, and 30 percent, respectively. What is the probability that all of these bonds will default in the next three years if the individual default probabilities are independent? A. 1.44%. B. 0.14%. C. 23.00%. D. 46.00%. Question 21 Which of the following statements about the correlation coefficient is TRUE? The correlation coefficient is: A. boundless. B. bounded between-1 and 0. C. bounded between 0 and +1. D. bounded between-1 and +1. ________________________________________ Question 22 Let A and B be two mutually exclusive events with P(A) = 0.40 and P(B) = 0.20. Therefore: A. P(A and B) = 0. B. P(B| A) = 0.20. C. P(A or B) = 0.52. D. P(A and B) = 0.08. Question 23 A joint probability of A and B must always be: A. less than or equal to the conditional probability of A given B. B. greater than or equal to the conditional probability of A given B. C. greater than or equal to than the probability of A or B. D. less than the probability of A and the probability of B. Question 24 Dependent random variables are defined as variables where their joint probability is: A. not equal to the product of their individual probabilities. 5-26 B. equal to zero. C. greater than the product of their individual probabilities. D. equal to the product of their individual probabilities. Question 25 A casual laborer has a 70 percent chance of finding work on each day that she reports to the day labor marketplace. What is the probability that she will work three days out of five? A. 0.3192. B. 0.5165. C. 0.3087. D. 0.6045. Question 26 X = 1 X = 2 Y = 1 0.05 0.15 Y = 2 0.15 0.15 Y = 3 0.20 0.30 Part 1) The expected value of X is closest to: A. 1.5 B. 1.2 C. 1.8 D. 1.6 Part 2) If you know that X is equal to 1, the probability that Y is equal to 2 is closest to: A. 0.38 B. 0.50 C. 0.15 D. 0.30 Part 3) The variance of Y is closest to: A. 2.27 B. 1.51 C. 0.61 D. 0.76 Question 27 The characteristic function of the product of independent random variables is equal to the: A. square root of the product of the individual characteristic functions. B. exponential root of the product of the individual characteristic functions. C. product of the individual characteristic functions. D. sum of the individual characteristic functions. Question 28 Consider a binomially distributed random variable that takes on one value with probability p and 6-26 the opposing value with probability q=1-p. For a large sample of n observations drawn from the population, the sampling distribution of proportions is approximately normal with a variance of: A. pq/n B. pq C. pqn D. pn Question 29 Which of the following statements about a normal distribution is least likely accurate? A. The mean, median, and mode are equal. B. The mean and variance completely define a normal distribution. C. Approximately 68% of the observations lie within +/- 1 standard deviation of the mean. D. A normal distribution has excess kurtosis of three. Question 30 For a normal distribution, what approximate percentage of the observations falls within ?2 standard deviations of the mean? A. 99%. B. 92%. C. 95%. D. 90%. Question 31 The lower limit of a normal distribution is: A. zero. B. negative infinity. C. one. D. negative one. Question 32 A group of investors wants to be sure to always earn at least a 5 percent rate of return on their investments. They are looking at an investment that has a normally distributed probability distribution with an expected rate of return of 10 percent and a standard deviation of 5 percent. What is the probability of meeting or exceeding the investors' desired return in any given year? A. 97.5%. B. 84.0%. C. 34.0%. D. 50.0%. Question33 A study of hedge fund investors found that their household incomes are normally distributed with a mean of $280,000 and a standard deviation of $40,000. Part 1) The percentage of hedge fund investors that have incomes greater than $350,000 is closest to: 7-26 A. 5.0%. B. 4.0%. C. 25.0%. D. 3.0%. Part 2) The percentage of hedge fund investors with income less than $180,000 is closest to: A. 1.15%. B. 2.50%. C. 0.62%. D. 6.48%. Question 34 For a continuous random variable X, the probability of any single value of X is: A. one. B. zero. C. determined by the cumulative function. D. determined by the probability density function (pdf). Question 35 If n is very large and p is small, the Poisson distribution may be used to approximate the binomial distribution with: A. λ=np(1-p). B. λ=n/p. C. D. λ=np. Question 36 Which of the following statements about probability distributions is FALSE? A. In a binomial distribution each observation has only two possible outcomes that are mutually exclusive. B. A probability distribution is a listing of all the possible outcomes of an experiment. C. A probability distribution is, by definition, normally distributed. D. One of the key properties of a probability function is 0 ? p ? 1. Question 37 Which of the following statements about the normal probability distribution is TRUE? A. The normal curve is asymmetrical about its mean. B. The standardized normal distribution has a mean of zero and a standard deviation of 10. C. Five percent of the normal curve probability falls more than outside two standard deviations from the mean. D. Sixty-eight percent of the area under the normal curve falls between 0 and +1 standard deviations above the mean. 8-26 Question 38 A random variable follows a continuous uniform distribution over 27 to 89. What is the probability of an outcome between 34 and 38? A. 0.0546. B. 0.0645. C. 0.0719. D. 0.0620. Question 39 A random variable X is continuous and bounded between zero and five, X:(0?X?5). The cumulative distribution function (cdf) for X is F(x)=x/5. Calculate P(2?X?4). A. 1.00. B. 0.25. C. 0.40. D. 0.50. Question 40 Probability distribution of a discrete random variable X X 0 1 2 3 4 5 6 7 P(X) 0.04 0.11 0.18 0.24 0.14 0.17 0.09 0.03 Part 1) The probability that X = 3 is: A. 0.18. B. 0.43. C. 0.24. D. 0.70. Part 2) The cdf of 5, or F(5), is: A. 0.71. B. 0.88. C. 0.17. D. 0.14. Part 3) The probability that X is greater than 3 is: A. 0.24. B. 0.43. C. 0.57. D. 0.67. Part 4) What is P (2 ? X ? 5)? A. 0.38. B. 0.73. C. 0.17. D. 0.12. 9-26 Question41 Given the probabilities N(-0.5) = 0.3085, N(0.75) = 0.7734, and N(1.50) = 0.9332 from a z-table, the probability of 0.2266 corresponds to: A. N(-0.75). B. N(-0.25). C. N(0.25). D. N(0.50). Question 42 If a random variable x is lognormally distributed then ln x is: A. abnormally distributed. B. the antilog of x. C. defined as ex. D. normally distributed. Question43 A normal distribution can be completely described by its: A. skewness and kurtosis. B. mean and variance. C. mean and mode. D. standard deviation. Question 44 Approximately 50 percent of all observations for a normally distributed random variable fall in the interval: A. B. C. D. Question 45 Standardizing a normally distributed random variable requires the: A. mean, variance and skewness. B. natural logarithm of X. C. mean and the standard deviation. D. variance and kurtosis. Question 46 Which of the following statements about probability distributions is FALSE? A. A discrete random variable is a variable that can assume only certain clearly separated values resulting from a count of some set of items. 10-26 B. A binomial probability distribution is an example of a continuous probability distribution. C. A continuous random variable is a quantity resulting from a random experiment that by chance can assume an infinite number of different values. D. The skewness of a normal distribution is zero. Question 47 A very large company has twice as many male employees relative to female employees. If a random sample of four employees is selected, what is the probability that all four employees selected are female? A. 0.0625. B. 0.0123. C. 0.3333. D. 0.6667. Question48 In a skewed distribution, what is the minimum amount of observations that will fall between +/- 1.5 standard deviations from the mean? A. 95%. B. 44%. C. 25%. D. 56%. Question 49 Return, R Frequency -10% up to 0% 0% up to 10% 10% up to 20% 20% up to 30% 30% up to 40% 3 7 3 2 1 Part 1) The number of intervals in this frequency table is: A. 5. B. 1. C. 16. D. 50. Part 2) The sample size is: A. 1. B. 5. C. 50. D. 16. 11-26 Part 3) The relative frequency of the second class is: A. 10.0%. B. 0.0%. C. 16.0%. D. 43.8%. Question50 In a negatively skewed distribution, what is the order (from lowest value to highest) for the distribution’s mode, mean, and median values? A. Mode, mean, median. B. Median, mode, mean. C. Median, mean, mode. D. Mean, median, mode. Question 51 A distribution of returns that has a greater percentage of small deviations from the mean and a greater percentage of extremely large deviations from the mean: A. is positively skewed. B. has positive excess kurtosis. C. is a symmetric distribution. D. has negative excess kurtosis. Question 52 When the tails of a distribution are fatter than that implied by a normal distribution, we say that the distribution is: A. leptokurtic. B. platykurtic. C. symmetrical. D. skewed. Question 53 What is the compound annual growth rate for stock A which has annual returns of 5.60 percent, 22.67 percent, and ?.23 percent? A. 6.00%. B. 8.72%. C. 17.44%. D. 7.08%. Question 54 XYZ Corp. Annual Stock Prices 1995 1996 1997 1998 1999 2000 22% 5% -7% 11% 2% 11% Part 1) 12-26 What is the mean return for XYZ stock? A. 8.0%. B. 7.3%. C. 11.0%. D. -7.0%. Part 2) Assuming that the distribution of XYZ stock returns is a population, what is the population variance (in %2)? A. 5.0. B. 6.8. C. 7.7. D. 80.2. Part 3) Assuming that the distribution of XYZ stock returns is a population, what is the population standard deviation? A. 5.02%. B. 8.96%. C. 6.84%. D. 46.22%. Part 4) Assuming that the distribution of XYZ stock returns is a sample, what is the sample variance (in %2)? A. 96.3. B. 5.0. C. 7.4. D. 72.4. Part 5) Assuming that the distribution of XYZ stock returns is a sample, what is the sample standard deviation? A. 7.4%. B. 72.4%. C. 9.8%. D. 96.3%. Question 55 Which of the following indicates the frequency of an interval in a frequency distribution histogram? A. Horizontal logarithmic scale. B. Width of the corresponding bar. C. Height multiplied by the width of the corresponding bar. D. Height of the corresponding bar. Question 56 How is the relative frequency of an interval computed? 13-26 A. B. C. D. By dividing the sum of the two interval limits by 2. By dividing the frequency of that interval by the sum of all frequencies. By multiplying the frequency of the interval by 100. By subtracting the lower limit of the interval by the upper limit. Question 57 In a positively skewed distribution, what is the order (from lowest value to highest) for the distribution’s mode, mean, and median values? A. Mode, mean, median. B. Mean, median, mode. C. Median, mean, mode. D. Mode, median, mean. Question 58 A summary measure that is computed to describe a population characteristic from a sample is called a: A. census. B. statistic. C. summary. D. parameter. Question 59 For a skewed distribution, what percentage of the observations will lie between ?2.5 standard deviations of the mean based on Chebyshe’s inequality? A. 16%. B. 56%. C. 75%. D. 84%. Question 60 Which of the following indicates the frequency of an interval in a frequency distribution histogram? A. A horizontal logarithmic scale. B. The width of the corresponding bar. C. The height of the corresponding bar. D. The height multiplied by the width of the corresponding bar. Question 61 Assuming a sample size of 40, which of the following is closest to the standardized value for a sample mean equal to 18 if the population from which the sample was taken has a mean and variance equal to 20 and 225, respectively? A. -0.8433. B. -0.5622. C. -0.3556. 14-26 D. 5.3333. Question 62 A distribution that has positive excess kurtosis: A. is less peaked than a normal distribution. B. has thinner tails than a normal distribution. C. is more skewed than a normal distribution. D. is more peaked than a normal distribution. Question 63 According to Chebyshev’s Inequality, for any distribution, what is the minimum percentage of observations that lie within three standard deviations of the mean? A. 56% B. 75%. C. 89%. D. 94%. Question 64 Which measure of central tendency can be used for both numerical and categorical variables? A. Mean. B. Median. C. Variance. D. Mode. Question 65 Which of the following statements about skewness and kurtosis is FALSE? I. Kurtosis is measured using deviations raised to the fourth power. II. Positive values of kurtosis indicate a distribution that has fat tails, referred to as platykurtic. III. Values of relative skewness in excess of 0.5 in absolute value indicate large levels of skewness. IV. Relative skewness is equal to the absolute skewness divided by the cubed standard deviation. A. I and II. B. II and III. C. II only. D. I and IV. Question66 Left-skewed distributions exhibit: A. greater mass to the left of the expected value. B. greater mass to the right of the expected value. C. a longer tail to the right of the distribution. D. greater mass close to the expected value. 15-26 Question 67 The sample mean is a consistent estimator of the population mean because the: A. expected value of the sample mean is equal to the population mean. B. sampling distribution of the sample mean has the smallest variance of any other unbiased estimators of the population mean. C. sampling distribution of the sample mean is normal. D. sample mean provides a more accurate estimate of the population mean as the sample size increases. Question68 A population’s mean is 30 and the mean of a sample of size 100 is 28.5. The variance of the sample is 25. What is the standard error of the sample mean? A. 0.05. B. 0.50. C. 0.25. D. 2.50. Question 69 A population has a mean of 20,000 and a standard deviation of 1,000. Samples of size n = 2,500 are taken from this population. What is the standard error of the sample mean? A. 20.00. B. 0.04. C. 400.00. D. 8.00. Question 70 What is the appropriate test statistic for constructing confidence intervals for the population mean of a normal distribution when the population variance is unknown? A. The t-statistic at α/2 with n degrees of freedom. B. The z-statistic with n -1 degrees of freedom. C. The z-statistic at α with n degrees of freedom. D. The t-statistic at α/2 with n -1 degrees of freedom. Question 71 If Estimator A is a more efficient estimator than Estimator B, it will have: A. a smaller mean and the same variance. B. a smaller mean and a larger variance. C. the same mean and a smaller variance. D. the same mean and a larger variance. Question 72 Which of the following statements about sampling and estimation is most accurate? A. The standard error of the sample means when the standard deviation of the population is 16-26 unknown equals s / B. The standard deviation of the distribution of the sample means is the standard error of the residual. C. The standard error of the sample means when the standard deviation of the population is known equals σ , where σ = sample standard deviation adjusted by n-1. D. The probability that a parameter lies within a range of estimated values is given by α. Question 73 The average U.S. dollar/Euro exchange rate from a sample of 36 monthly observations is $1.00/Euro. The population variance is 0.49. What is the 95 confidence interval for the mean U.S. dollar/Euro exchange rate? A. $0.5100 to $1.4900. B. $0.8075 to $1.1925. C. $0.8657 to $1.1343. D. $0.7713 to $1.2287. Question 74 What is the approximate 99 percent confidence interval for the population mean based on a sample of 60 returns with a mean of 7 percent and a sample standard deviation of 25 percent? A. 1.584% to 14.584%. B. 0.546% to 13.454%. C. -1.584% to 15.584%. D. 1.546% to 13.454%. Question 75 From a population of 5,000 observations, a sample of n = 100 is selected. Calculate the standard error of the sample mean if the population standard deviation is 50. A. 4.48. B. 5.00. C. 4.00. D. 50.00. Question 76 An equity analyst needs to select a representative sample of manufacturing stocks. Starting with the population of all publicly traded manufacturing stocks, she classifies each stock into one of the 20 industry groups that form the Index of Industrial Production for the manufacturing industry. She then selects a number of stocks from each industry based on its weight in the index. The sampling method the analyst is using is best characterized as: A. data mining. B. nonrandom sampling. C. simple random sampling. D. stratified random sampling. 17-26 Question 77 The Central Limit Theorem states that, for any distribution, as n gets larger, the sampling distribution: A. becomes larger. B. becomes smaller. C. approaches a normal distribution. D. approaches the mean. Question78 If the variance of the sampling distribution of an estimator is smaller than all other unbiased estimators of the parameter of interest, the estimator is: A. reliable. B. unbiased. C. efficient. D. consistent. Question 79 A sample of size 25 is selected from a normal population. This sample has a mean of 15 and the population variance is 4. Using this information, construct a 95 percent confidence interval for the population mean, m. A. 15 + 1.96(2). B. 15 + 1.96(0.4). C. 15 + 1.96(0.8). D. 15 + 1.96(4). Question 80 The central limit theorem concerns the sampling distribution of the: A. sample mean. B. population mean. C. sample standard deviation. D. population standard deviation. Question81 The sample mean is an unbiased estimator of the population mean because the: A. sampling distribution of the sample mean has the smallest variance of any other unbiased estimators of the population mean. B. sample mean provides a more accurate estimate of the population mean as the sample size increases. C. sampling distribution of the sample mean is normal. D. expected value of the sample mean is equal to the population mean. Question82 If n is large and the population standard deviation is unknown, the standard error of the sampling 18-26 distribution of the sample mean is equal to the: A. population standard deviation divided by the sample size. B. population standard deviation multiplied by the sample size. C. sample standard deviation divided by the square root of the sample size. D. sample standard deviation divided by the sample size. Question83 An analyst divides the population of U.S. stocks into 10 equally sized sub-samples based on market value of equity. Then he takes a random sample of 50 from each of the 10 sub-samples and pools the data to create a sample of 500. This is an example of: A. simple random sampling. B. complex normal sampling. C. systematic cross-sectional sampling. D. stratified random sampling. Question 84 Joseph Lu calculated the average return on equity for a sample of 64 companies. The sample average is 0.14 and the sample standard deviation is 0.16. The standard error of the mean is closest to: A. 0.0200. B. 0.1600. C. 0.0025. D. 0.0500. Question 85 To apply the central limit theorem to the sampling distribution of the sample mean, the sample is usually considered to be large if n is greater than: A. 30. B. 15. C. 20. D. 25. Question 86 The mean equity risk premium over a 40-year period is equal to 8.0 percent. The standard deviation of the sample is 12 percent. The standard error of the sample mean is closest to: A. 0.30%. B. 1.90%. C. 1.26%. D. 8.00%. Question 87 You have collected monthly returns for a mutual fund and want to test the null hypothesis that the standard deviation exceeds the advertised standard deviation of 3.5 percent. The most appropriate test statistic is based on a: 19-26 A. B. C. D. F-test. t-test. z-test. chi-square test. Question 88 A Type I error occurs when the null hypothesis: A. is rejected when it is true. B. fails to be rejected when it is false. C. is rejected when it is false. D. fails to be rejected when it is true. Question89 Which of the following is the correct sequence of events for testing a hypothesis? A. State the hypothesis, formulate the decision rule, select the level of significance, compute the test statistic, and make a decision. B. State the hypothesis, select the level of significance, compute the test statistic, formulate the decision rule, and make a decision. C. State the hypothesis, select the level of significance, formulate the decision rule, compute the test statistic, and make a decision. D. State the hypothesis, formulate the decision rule, compute the test statistic, select the level of significance, and make a decision Question 90 In a two-tailed hypothesis test, Jack Olson computes a t-statistic of 2.7 based on a sample of 20 observations where the distribution is normal. If a 5 percent significance level is chosen, Olson should: A. not make a conclusion pending additional observations. B. reject the null hypothesis and conclude that the population mean is not significantly different from zero. C. fail to reject the null hypothesis that the population mean is not significantly different from zero. D. reject the null hypothesis and conclude that the population mean is significantly different from zero. Question 91 Which of the following statements about hypothesis testing is FALSE? A. If the alternative hypothesis is Ha: µ> µ0, a two-tailed test is appropriate. B. The null hypothesis is a statement about the value of a population parameter. C. A Type II error is failing to reject a false null hypothesis. D. A Type I error is rejecting the null hypothesis when it is actually true. Question 92 The test statistic for an F-test of the equality of two sample variances is the: 20-26 A. B. C. D. ratio of the two sample variances. product of the two sample variances. ratio of the two sample standard deviations. product of the two sample standard deviations. Question 93 A goal of an innocent until proven guilty justice system is to place a higher priority on: A. avoiding type II errors. B. avoiding type III errors. C. the null hypothesis. D. avoiding type I errors. Question 94 Which of the following statements is FALSE? A. A Type I error is rejecting the null when it is actually true. B. If a person is presumed innocent unless proven otherwise, finding a guilty person innocent is an example of a Type II error. C. Failing to reject the null when it is false is an example of a Type II error. D. The probability of committing a Type I error is the significance level of the test. Question 95 The sampling distribution of variances is described by which distribution? A. Normal distribution. B. Student’s t-distribution. C. F-distribution. D. Chi-square distribution. Question 96 A Type I error: A. rejects a true null hypothesis. B. rejects a false null hypothesis. C. fails to reject a false null hypothesis. D. fails to reject a true null hypothesis. Question 97 An analyst is conducting a hypothesis test to determine if the mean time spent on investment research is different from 3 hours per day. The test is performed at the 5 percent level of significance and uses a random sample of 64 portfolio managers, where the mean time spent on research is found to be 2.5 hours. The population standard deviation is 1.5 hours. Part 1) The appropriate null hypothesis for the described test is: A. H0: µ ? 3 hours. B. H0: µ ? 3 hours. C. H0: µ = 3 hours. 21-26 D. H0: µ ? 3 hours. Part 2) Which type of test is this? A. One-tailed test. B. Two-tailed test. C. Chi-square test. D. Equity of variance test. Part 3) The calculated z-statistic is: A. -2.13. B. -2.67. C. +0.33. D. +2.67. Part 4) The critical z-value(s) of the test statistic is (are): A. -1.96. B. ? 1.96. C. +1.96. D. ? 2.58. Part 5) Which of the following decisions is the CORRECT decision for this study? A. Fail to reject the null hypothesis. B. Reject the null hypothesis. C. The sample size is too small, so increase the sample size. D. No decision is possible because the sample standard deviation was not given. Question 98 Margo Hinsdale is testing the null hypothesis that the population mean is less than or equal to 45. A random sample of 81 observations selected from this population produced a mean of 46.3. The population has a standard deviation of 4.5. Part 1) The value of the appropriate test statistic for the test of the population mean is: A. z =-2.75. B. t = 3.84. C. z = 2.60. D. t = 4.60. Part 2) At a 1 percent level of significance, the correct decision is to: A. accept the null hypothesis. B. reject the null hypothesis. C. fail to reject the null hypothesis. D. neither reject nor fail to reject the null hypothesis. Question 99 In order to test if Stock A is more volatile than Stock B, prices of both stocks are observed to construct the sample variance of the two stocks. The appropriate test statistics to carry out the test is the: A. F test. B. t test. C. Z test. D. Chi-square test. Question100 The first step in the process of hypothesis testing is: A. the collection of the sample. B. the calculation of sample statistics. C. selecting the test statistic. D. to state the hypotheses. Question 101 A return series with 250 observations has a sample mean of 10 percent and a standard deviation of 15 percent. The standard error of the sample mean is closest to: A. 0.06. B. 15.80. C. 0.95. D. 3.87. Question 102 Brian Ci believes that the average return on equity in the airline industry, µ, is less than 5 percent. What are the appropriate null (H0) and alternative (Ha) hypotheses to test this belief? A. H0: µ ? 0.05 versus Ha: µ < 0.05. B. H0: µ < 0.05 versus Ha: µ > 0.05. C. H0: µ > 0.05 versus Ha: µ < 0.05. D. H0: µ < 0.05 versus Ha: µ ? 0.05. Question 103 If the sample size is greater than 30 and population variance is unknown, the appropriate test for the sample mean is the: A. t-test or z-test. B. t-test. C. z-test. D. p-test or F-test. Question104 SCU and QXA are two stocks in the same industry. The variance of returns for each stock is 0.3025 and the returns are perfectly positively correlated. The covariance between the returns is closest to: A. B. C. D. 0.3025. 0.1000. 0.2525. 0.5500. Question 105 Consider a sample of 32 observations on variables X and Y in which the correlation is 0.30. If the level of significance is 5 percent, we: A. conclude that there is significant correlation between X and Y. B. conclude that there is little correlation between X and Y. C. conclude that there is no significant correlation between X and Y. D. cannot test the significance of the correlation with this information. Question 106 The standard error of estimate is closest to the: A. standard deviation of the dependent variable. B. standard deviation of the residuals. C. standard deviation of the independent variable. D. percent of variations of the dependent variable. Question107 Which model does not lend itself to correlation coefficient analysis? A. Y = X + 2. B. X = Y × 2. C. Y = X3. D. Y -X = 2. Question 108 The purpose of regression is to: A. explain the variation in the dependent variable. B. explain the variation in the independent variable. C. get the largest R2 possible. D. explain the mean of the independent variable. Question109 In order to have a negative correlation between two variables, which of the following must be TRUE? A. Either the covariance or one of the standard deviations must be negative. B. Both the covariance and at least one of the standard deviations must be negative. C. The covariance must be negative. D. The covariance can never be negative. Question 110 Which of the following statements about covariance and correlation is FALSE? A. A zero covariance implies a zero correlation. B. A positive covariance is indicated by an upward sloping relation in the points on the scatter plot of the two variables. C. The covariance and correlation are always the same sign, positive or negative. D. There is no relation between the sign of the covariance and the correlation. Question 111 Sera Smith, a research analyst, had a hunch that there was a relationship between the percentage change in a firm’s number of salespeople and the percentage change in the firm’s sales during the following period. Smith ran a regression analysis on a sample of 50 firms, which resulted in a slope of 0.72, an intercept of +0.01, and an R-squared value of 0.65. Based on this analysis, if a firm made no changes in the number of sales people, what percentage change in the firm抯 sales during the following period does the regression model predict? A. +0.72%. B. +0.65%. C. +0.10%. D. +1.00%. Question112 Consider a sample of 60 observations on variables X and Y in which the correlation is 0.42. If the level of significance is 5 percent, we: A. conclude that there is no significant correlation between X and Y. B. conclude that there is statistically significant correlation between X and Y. C. conclude that there is little correlation between X and Y. D. cannot test the significance of the correlation with this information. Question 113 The capital asset pricing model is given by: Ri=Rf+Beta(Rm?Rf),where Rm= expected return on the market, Rf= risk-free market and Ri = expected return on a specific firm. The dependent variable in this model is: A. B. C. D. Rf Rm. Ri Rm?Rf. ________________________________________ Question 114- Which term does NOT apply to a regression model? A. Coefficient of variation. B. Goodness of fit. C. R Square. D. Coefficient of determination. ________________________________________ Question 115 Paul Frank is an analyst for the retail industry. He is examining the role of television viewing by teenagers on the sales of accessory stores. He gathered data and estimated the following regression of sales (in millions of dollars) on the number of hours watched by teenagers (in hours per week): Salest = 1.05 + 1.6 TVt Which of the following is a CORRECT interpretation of the estimated results? If TV watching: A. goes up by one hour per week, sales of accessories increase by $1.60. B. changes, no change in sales is expected. C. is zero (that is, every teenager turns off the TV for a week), the expected sales of accessories is $0. D. goes up by one hour per week, sales of accessories increase by $1.6 million. Question 116 The independent variable in a regression equation is called all of the following EXCEPT: A. explanatory variable. B. exogenous variable. C. predicting variable. D. predicted variable. Question117 In an ordinary least squares regression, t-tests are used to determine the statistical significance of: A. the individual parameter estimates. B. the regression. C. a set of parameters. D. the error term.