CFA Institute CFA Institute Certifications CFA-LEVEL-1 Questions & Answers

• Question 3461:

  A study of a company's practice regarding the payment of invoices revealed that on the average an invoice was paid 20 days after it was received. The standard deviation equaled five days. Assuming that the distribution is normal, what percent of the invoices were paid within 15 days of receipt?

  A. 37.91%

  B. 86.74%

  C. 15.87%

  D. 34.13%

  E. None of these answers

  Correct Answer: C

  z = (x-u)/sigma = 15 - 20/5 = -1.0. z = 1 is 0.3413. 1.0 - 0.8413 = 0.1587.

• Question 3462:

  If the correlation coefficient between two variables equals zero, what can be said of the variables X and Y?

  A. Highly correlated

  B. Not correlated

  C. Dependent on each other

  D. None of these answers are correct

  E. All of these answers are correct

  Correct Answer: B

  r ranges from -1 to +1. The closer it is to -1 or +1, the stronger the relationship. Closer it is to zero, the weaker.

• Question 3463:

  You believe the stock of Microsquish reflects a 90% chance of a dismissal of its contractual liability suit. If the suit is dismissed, you expect the stock of Microsquish and its partner, AWOL, to rise. If the suit is not dismissed, both will fall in price. However, you think that AWOL's stock only reflects a 60% chance of dismissal of this suit. What strategy would be optimal?

  A. Sell both short

  B. Buy Microsquish

  C. Sell AWOL

  D. Buy AWOL

  Correct Answer: D

  This is an example of the investment consequences of inconsistent probabilities. If the true probability of a lawsuit dismissal is only 60%, then AWOL's stock is fairly valued, and Microsquish is overvalued. If the true probability is 90%, then Microsquish is fairly valued, and AWOL is undervalued. Your can thus construct a profitable risk-free strategy. You should buy AWOL, because at worst, the stock will be fairly valued. At best, it is undervalued. You could also simultaneously short Microsquish, because at best, it is fairly valued; there is a chance that it is overvalued. Note that this example ignores all other factors other than the lawsuit.

• Question 3464:

  A cumulative frequency distribution on days absent during a calendar year by employees of a manufacturing company is shown below. Days Absent Cumulative Number of Employees 0 - 260 3 - 531 6 - 814 9 - 116 12 - 142 How many employees were absent more than five days?

  A. 14

  B. 8

  C. None of these answers

  D. 22

  E. 31

  Correct Answer: A

  The cumulative number for class 6-8 will give us the number of people absent more than five days; 14.

• Question 3465:

  Tran Holten, a quantitative analyst with Smith, Kleen and Beetchnutty Brokerage, has just been informed of an important error in one of his recent statistical endeavors. Specifically, in one hypothesis test, Mr. Holten rejected a null hypothesis that later was proven to be true. Which of the following best describes this type of error in hypothesis testing? Further, if the confidence level of the test were increased, would the probability of this error increase, decrease, or remain unchanged?

  A. Type I error; decrease

  B. Type I error; increase

  C. Type II error; decrease

  D. Type I error; remain unchanged

  E. Type II error; remain unchanged

  F. Type II error; increase

  Correct Answer: A

  In this example, Tran Holten has incorrectly rejected a null hypothesis. This type of error in hypothesis testing is called a Type I error. In hypothesis testing, the Type I error is given much more attention than the Type II error. In most hypothesis tests, the probability of a null hypothesis is equal to the significance level of the test. A significance level of 0.01, for example, indicates that a 1% chance exists that the null hypothesis will be rejected when it is indeed true. Another way to think of the probability of a Type I error is

  to observe the following relationship:

  {Probability of a Type I error = (1 - confidence level)}.

  For example, a confidence level of 95% leaves a 5% probability of a Type I error occurring. If this

  confidence level were to increase to say, 98%, then the probability of a Type I error would reduce to 2%.

  As you can see, there is a relationship between the confidence level of a test and the probability of a Type

  I error. If the confidence level of the test in this example were to increase, then the probability of a Type I

  error would decrease.

• Question 3466:

  If you deposit $10,000 into an account paying 6% per year, compounded semiannually, how much do you have in the account in 8 years?

  A. $15,938.48

  B. $16,047.06

  C. $12,667.70

  D. $14,800.00

  E. $25,403.52

  Correct Answer: B

  On the BAII Plus, press 16 N, 6 divide 2 = I/Y, 10000 PV, 0 PMT, CPT FV. On the HP12C, press 16 n, 6 ENTER 2 divide i, 10000 PV, 0 PMT, FV. Note that the answer will be displayed as a negative number. Make sure the BAII Plus has the value of P/Y set to 1.

• Question 3467:

  The semiannually compounded rate is 10% quoted on an annualized basis. The equivalent annually compounded rate is:

  A. 10.25%

  B. 10.5%

  C. 9.65%

  D. 10.1%

  Correct Answer: A

  To solve such problems, think about investing a dollar for a year. The final amount should be the same under both the quotations. Under annually compounded rate, r, $1 grows to 1+r in 1 year. Under semiannual compounding, it grows to (1 +0.1/2)^2 = 1.1025. Since these two should be equal, we get 1+r = 1.1025, giving r = 10.25%. Note that the annually compounded rate must be larger than the semiannually rate, ruling out 9.65 automatically.

• Question 3468:

  In hypotheses testing, what is the level of significance?

  A. Symbolized by the Greek letter "alpha"

  B. All of these answers are true

  C. Selected before a decision rule can be formulated

  D. Value between 0 and 1

  E. Risk of rejecting the null hypothesis when it is true

  Correct Answer: B

  All the above a correct descriptions of the level of significance.

• Question 3469:

  A random variable can take on four values: 12, 36, 78, 111, each with probability 0.25. The standard deviation of the random variable equals ________.

  A. 152.4

  B. 49.3

  C. 1,451

  D. 38.1

  Correct Answer: D

  Since all the observations occur with equal probability, the mean of the observations is (12 + 36 + 78 + 111)*0.25 = 59.25. The variance is then given by 0.25*( [12-59.25]^2 + [36-59.25]^2 + [78-59.25]^2 + [11159.25]^2) = 1451. The standard deviation is equal to sqrt(1451) = 38.1.

• Question 3470:

  Which measure of dispersion disregards the algebraic signs (plus and minus) of each difference between X and the mean?

  A. Standard deviation

  B. Variance

  C. Mean deviation

  D. Mean

  E. None of these answers

  Correct Answer: C

  The mean deviation is the mean of the absolute values of the deviations from the mean.