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

• Question 3271:

  A sample of the paramedical fees charged by clinics revealed these amounts: $55, $49, $50, $45, $52 and $55. What is the median charge?

  A. None of these answers

  B. $51.00

  C. $47.50

  D. $52.00

  E. $55.00

  Correct Answer: B

  Order them: 45,49,50,52,55,55. The median is therefore (50 + 52)/2 = 51

• Question 3272:

  A sample of 10 observations is drawn from a population with mean 17. The mean of the observations equals 14.3 and the sample standard deviation equals 4.8. The sampling error in mean equals ________.

  A. 9.6

  B. -2.7

  C. 14.3

  D. 4.8

  Correct Answer: B

  "Sampling error" refers to the difference between a sample statistic and the corresponding population parameter. In this case, the sampling error equals 14.3 - 17 = -2.7.

• Question 3273:

  If all the 10,000 data points in a regression lie exactly on a straight line, which of the following is/are true?

  I. The intercept term is zero.

  II. The percentage of unexplained variance equals zero

  III. The slope coefficient is positive.

  IV.

  The correlation coefficient between the dependent and independent variables is 1.

  A.

  III only

  B.

  IV only

  C.

  II and IV

  D.

  III and IV

  E.

  II only

  F.

  I only

  Correct Answer: E

  Since there is no error in the regression, the percentage of unexplained variance will be zero. The intercept and slope terms can be any real numbers and the correlation coefficient will be either + 1 or - 1.

• Question 3274:

  You are given n = 12, sum of the (X_i) = 2%, sum of the (X_i)^2 = 0.5%%. Find the sample standard deviation.

  A. 1.27%.

  B. 1.73%.

  C. 1.23%.

  D. 1.11%.

  Correct Answer: C

  The sample standard deviation will be the positive square root of the sample variance. The sample variance will be determined using the computational formula [1/(n-1)] * {sum (as i goes from 1 to n) of (X_i) ^2 - (1/n) * [sum (as i goes from 1 to n) of (X_i)]^2}. So we get 1/11 * (0.5 - 1/12*(2^2)) = 1.51%%. The positive square root of 1.51%% is 1.23%.

• Question 3275:

  Sharleef Nettleton, a quantitative analyst with Churn Brothers Brokerage, is examining a data sample and has amassed the following information: Standard deviation of the sample: 2.90 Number of observations: 68 Degrees of freedom: 2 Sample mean: 114 Assume that Ms. Nettleton formulates a null hypothesis that states that the value of the population mean is zero. Additionally, assume that the population standard deviation is unknown. Given this information, what is the standard error of the estimate? Further, what is the test statistic? Choose the best answer.

  A. 1.0199; 111.78

  B. 0.3517; 84.34

  C. 1.0199; 56.44

  D. 0.3517; 324.14

  E. None of these answers is correct.

  F. 0.3570; 29.91

  G. 0.3570; 319.38

  Correct Answer: D

  If the population standard deviation is unknown, as in this example, the standard error of the estimate is

  found by using the following equation:

  {Standard error = s / square root of n} where s = the sample standard deviation and n = the number of

  observations in the sample.

  In this example, all of the necessary information has been provided, and the determination of the standard

  error of the estimate is found as:

  {Standard error = [2.90 / 8.2462] = 0.3517}

  Now that the standard error of the estimate has been calculated, the test statistic can be found by using

  the following equation:

  {Test statistic = [sample statistic - value of the population parameter under the null hypothesis] / standard

  error of the sample statistic].

  Again, all of the necessary information has been provided, and the calculation of the test statistic is found

  as follows:

  {Test statistic = [114 - 0] / 0.3517 = 324.14}

  This is a very large test statistic and the null hypothesis will likely be rejected unless a very low level of

  confidence is employed.

• Question 3276:

  Which of the following is/are true?

  I. If a test always rejects the null, its significance level is zero.

  II. If a test always accepts the null, the probability of type II error equals zero.

  III.

  If the p-value exceeds the significance level, you cannot reject the null.

  A.

  II only

  B.

  I only

  C.

  III only

  D.

  II and III

  Correct Answer: C

  The lowest significance level at which the null hypothesis can be rejected is called the p-value of the test. Thus, if the p-value is less than the significance level, the null hypothesis can be rejected at that significance level; otherwise, you must fail to reject the null. The significance level in hypothesis testing refers to the probability that we will reject the null when it is true. Hence, if we always reject the null, the probability of rejecting it when it is true equals 1. A Type II error occurs when we fail to reject the null when in fact it is false. Therefore, if we always accept the null, we will never reject it even when it is false. So the probability of Type II error will equal 1.

• Question 3277:

  Delroy McWilliams, a quantitative analyst with Churn Brothers Brokerage, is examining a data sample and has amassed the following information:

  Standard deviation of the sample: 70 Number of observations: 600 Sample mean: 812

  Assume that Mr. McWilliams formulates a null hypothesis that states that the value of the population mean is equal to 800. Additionally, assume that the population standard deviation is unknown. Given this information, what is the standard error of the estimate? Further, what is the test statistic? Choose the best answer.

  A. 8.370; 1.434

  B. 8.370; 4.148

  C. None of these answers is completely correct.

  D. 0.014; 11.834

  E. 0.014; 857.143

  F. 2.858; 1.40

  G. 2.858; 11.60

  Correct Answer: C

  The standard error and test statistic for this example is 2.858 and 4.199, respectively. Therefore, none of

  these answers is correct. If the population standard deviation is unknown, as in this example, the standard

  error of the estimate is found by using the following equation:

  {Standard error = s / square root of n} where s = the sample standard deviation and n = the number of

  observations in the sample.

  In this example, all of the necessary information has been provided, and the determination of the standard

  error of the estimate is found as:

  {Standard error = [70 / 24.495] = 2.858}

  Now that the standard error of the estimate has been calculated, the test statistic can be found by using

  the following equation:

  {Test statistic = [sample statistic - value of the population parameter under the null hypothesis] / standard

  error of the sample statistic].

  Again, all of the necessary information has been provided, and the calculation of the test statistic is found

  as follows:

  {Test statistic = [812 - 800] / 2.858 = 4.199}

• Question 3278:

  Eternal Life Insurance has a policy that will pay $50,000 per year starting 20 years from now, to you and all your progeny. If the appropriate discount rate is 10% per year and you have to pay premiums every year for the next 15 years starting at the end of this year, what's the annual premium payment that you and your heirs must make for this to be a fair deal?

  A. $10,749

  B. $14,495

  C. $9,771

  D. $12,189

  Correct Answer: A

  You are entitled to a perpetuity which start paying 20 years from now. Therefore, at the end of year 19, you will have an asset worth $50,000/0.1 = $500,000. The present value of this equals $500,000/1.1^19 = $81,754. Your premium payments are a 15-year annuity. If the annual premium is P, then this annuity has a present value of P/0.1*[1 - 1/1.1^15] = 7.606P. This must equal the value of the perpetuity for this to be a fair deal. This gives P = $81,754/7.606 = $10,749.

• Question 3279:

  You are examining a group of 6 stocks. Their average annual standard deviations have been 25%, 20%, 15%, 25%, 16%, and 45%. What is the range of annual standard deviations?

  A. 25.0%.

  B. 15.0%.

  C. 30.0%.

  D. 29.0%.

  Correct Answer: C

  The range = the maximum value - the minimum value. Here, we have 45% - 15% = 30%.

• Question 3280:

  Routine physical examinations are conducted annually as part of a health service program for the employees. It was discovered that 8% of the employees needed corrective shoes, 15% needed major dental work and 3% needed both corrective shoes and major dental work. What is the probability that an employee selected at random will need either corrective shoes or major dental work?

  A. 0.20

  B. 1.00

  C. 0.25

  D. 0.50

  E. None of these answers

  Correct Answer: A

  8% + 15% - 3% = 20%