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

• Question 3151:

  A bell-shaped, symmetrical frequency distribution has a mean of 50. If 68% of the observations in the distribution fall between 40 and 60, what's the range within which 99% of the observations in the distribution fall?

  A. [19.79; 80.21]

  B. [23.1; 76.9]

  C. [30; 70]

  D. [24.2; 75.8]

  Correct Answer: D

  For a bell-shaped, symmetrical frequency distribution, approximately 68% of the observations lie within one standard deviation of the mean. The mean equals (40 + 60)/2 = 50. Therefore, the standard deviation equals 50 - 40 = 10. Now, by the normal rule, 99% of the observations lie within 2.58 standard deviations of the mean. Hence, the requisite range equals [50 - 2.58*10, 50 + 2.58*10] = [24.2, 75.8].

• Question 3152:

  The sampling distribution of the sampling mean is:

  A. the distribution of the means of all possible samples of a given size from a given population.

  B. the distribution of all possible samples of a given population.

  C. the distribution of all possible means of a given population.

  D. the distribution of the means of all possible samples of a given population.

  Correct Answer: A

  The sampling distribution of the sample means is a probability distribution of all possible sample means of a specific sample size.

• Question 3153:

  All possible samples of size n are selected from a population and the mean of each sample is determined. What is the mean of the sample mean?

  A. Cannot be estimated in advance

  B. None of these answers

  C. Exactly the same as the population mean

  D. Larger than the population mean

  E. Smaller than the population mean

  Correct Answer: C

  If we selected all possible samples from the population, then the sample mean will be equal to the population mean. Only when we cannot select all possible samples will be a difference.

• Question 3154:

  Armando Delrio, a quantitative analyst with Brown Brothers Brokerage, has been instructed to create a regression analysis comparing the relationship between same store sales figures for a batch of retail stocks and marketing expenses for the same series of stocks. In order to adhere to the traditional seven-step method of hypothesis testing, Armando should begin his analysis by performing which of the following actions? Choose the best answer.

  A. Formulating the hypothesis

  B. Collecting the data

  C. Stating the significance level

  D. None of these answers is correct

  E. Identifying the test statistic

  F. Identifying the probability distribution

  Correct Answer: A

  Hypothesis testing involves a series of seven explicit steps:

  Step 1: Formulating and stating the hypothesis Step 2: Identifying the appropriate test statistic and its probability distribution Step 3: Specifying the significance level Step 4: Stating the decision rule Step 5: Collecting the data and performing the necessary calculations Step 6: Making the statistical decision Step 7: Making the economic/investment decision.

  In this example, Armando Delrio, a quantitative analyst, has been instructed to perform a regression analysis in which a hypothesis is tested. The first step in this process is the formulation of the hypothesis.

• Question 3155:

  Which of the following is not a valid reason for selecting a sample instead of studying the whole population?

  A. All of these answers reasons are valid

  B. Sample results have more accuracy than population results

  C. Cost of studying an entire population can be too high

  D. Population can be destroyed in the process of studying it

  E. Study of the population can be too time consuming

  Correct Answer: B

  Sample results cannot be more accurate since it is based on a subset of the population.

• Question 3156:

  What annual interest rate, compounded annually, will cause an original deposit of $500 to grow to $625, after 3 years?

  A. 7.27%

  B. 9.14%

  C. 6.78%

  D. 7.72%

  E. 2.57%

  Correct Answer: D

  On the BAII Plus, press 500 PV, 625 +/- FV, 0 PMT, 3 N, then CPT I/Y. On the HP12C, press 500 PV, 625 CHS FV, 0 PMT, 3 n, then press i.

• Question 3157:

  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 never absent?

  A. None of these answers

  B. 29

  C. Cannot be determined from the given data

  D. 31

  E. 60

  Correct Answer: C

  We were given only the number of employees in the 0-2 group. So we do not know how many were never absent since this group includes those who were absent 1 and 2 days.

• Question 3158:

  Judging from recent experience, 5 percent of the worm gears produced by an automatic, high speed machine are defective. What is the probability that out of six gears selected at random, exactly zero gears will be defective?

  A. 0.500

  B. 0.167

  C. 0.735

  D. 0.001

  E. None of these answers

  Correct Answer: C

  Using Binomial probability with n = 6, p = 0.05 and q = 0.95 and r = 0 we get [6!(0.05^0)(0.95^6)]/0!(6 - 0)! = 0.735.

• Question 3159:

  The results of the regressions using 200 observation on a variable Y against X are as follows:

  Coefficient Standard error intercept 3.62.1 slope 8.11.3

  R square = 49%

  The percentage of variance in the dependent variable not explained by the regression equals ________.

  A. 36.4%

  B. 49%

  C. 18%

  D. 51%

  Correct Answer: D

  The R-square of the regression measures the amount of variance of the dependent variable explained by the independent variable. This is given to be 49%. Hence, the amount not explained equals 100% - 49% = 51%.

• Question 3160:

  What is the probability of making a Type II error if the null hypothesis is actually true?

  A. .05

  B. alpha

  C. 1

  D. 0

  E. none of these answers

  Correct Answer: D

  The type II error is accepting a null hypothesis when it is actually false. The probability of committing this error is called beta. Therefore the probability of making a type II error when the null is true is zero.