QUESTION: 1061

The sum of the squares of 65 observations equals 862. The sum of the observations equals 93. The sample

standard deviation of the observations equals ________.

11.21
1.43
3.37
4.96

Answer(s): C

Explanation:

For N observations, it is easy to show that
sample variance*(N-1) = (sum of squares) - N*(mean^2)
Hence, in this case, sample variance = (862 - 65*(93/65)^2)/64 = 11.39. The standard deviation then equals sqrt(11.39) = 3.37
Note: You should be careful about the difference between population variance and sample variance. The formula for population variance is:
population variance*N = (sum of squares) - N*(mean^2)
You can expect an exam question which asks for population variance, with the choices given containing both the population and the sample variances or vice versa.

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QUESTION: 1062

Which of the is/are true?

The probability of type II error equals 1 - significance level.
II. A higher significance level is makes it easier to reject a null hypothesis.
III. Minimizing the chance of a Type I error minimizes the probability of Type II error.
IV. The higher the probability of Type II error, the higher is the chance that the alternative will be accepted when it is true.
II & IV
IV only
I & IV
III & IV
II only
I only
I, II & IV
III only

Answer(s): A

Explanation:

The probability of Type I (not type II) error equals 1 - the significance level.
The significance level represents an upper bound on the probability that the null hypothesis is true given the observed sample. The higher this level is set, the easier it is to say that the null is false (though the probability that you are making a mistake in rejecting the null also becomes higher!).
Type I and Type II errors represent two different types of errors and are not directly related. A relationship like (III) appears tempting but is not true.
For the purposes of CFA Level I exam, (IV) can be taken to be true, though technically, it is not entirely accurate. It holds only if the alternative hypothesis is exactly complementary to the null hypothesis i.e. the null hypothesis and the alternative hypothesis span the entire range of values that the variable being tested can take. If you set up the alternative hypothesis incorrectly, then rejection of the null does not necessarily imply that the alternative is true; it could also imply that you have not taken all the possibilities into consideration. For e.g., suppose a theory does not rule out the possibility that a variable X can be negative but you mistakenly set up the hypotheses as Ho: X = 0, H1: X > 0. Then clearly, even if you reject the null hypothesis, it does not imply that X can take only positive values. Recognizing such mistakes in setting up a hypothesis test is crucial.

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QUESTION: 1063

What single deposit could you make today in order to have $1,000,000 in 30 years, assuming it earns interest at 11% per year, compounded monthly?

$403,512.59
$115,024.60
$9,523.23
$43,682.82
$37,441.83

Answer(s): E

Explanation:

On the BAII Plus, press 360 N, 11 divide 12 = I/Y, 0 PMT, 1000000 FV, CPT PV. On the HP12C, press 360 n, 11 ENTER 12 divide i, 0 PMT, 1000000 FV, PV. Note that the answer is displayed as a negative number. Make sure the BAII Plus has the value of P/Y set to 1.

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QUESTION: 1064

The probabilities and the number of automobiles lined up at a Lakeside Olds at opening time (7:30 a.m.) for service are:

Number Probability
10.05
20.30
30.40
40.25

On average, how many automobiles should Lakeside Olds expect to be lined up at opening?

None of these answers
1.
1.96
10.
2.85

Answer(s): E

Explanation:

1*0.05 + 2*0.30 + 3*0.40 + 4*0.25 = 2.85.

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QUESTION: 1063

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QUESTION: 1064

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