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# P1.T2.406. Distributions II

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Concept: These on-line quiz questions are not specifically linked to AIMs, but are instead based on recent sample questions. The difficulty level is a notch, or two notches, easier than bionicturtle.com's typical AIM-by-AIM question such that the intended difficulty level is nearer to an actual exam question. As these represent "easier than our usual" practice questions, they are well-suited to online simulation.

Questions:

406.1. A fund advertises that its maximum volatility is 10.0%. However, over the last 15 trading days (n = 15), the observed volatility is 14.0%. With 95.0% confidence, can we reject the null hypothesis that the true (population) volatility is equal to 10.0% or less? Please use this chi-square lookup table:
https://www.bionicturtle.com/images/2014/dailypq/406_1_chi_square.png.

a. No, fail to reject this one-tailed null due to an observed chi-square value of 19.60 which is less than the one-tailed 5.0% critical chi-square
b. No, fail to reject this one-tailed null due to an observed chi-square value of 38.57 which is less than the one-tailed 5.0% critical chi-square
c. Yes, reject this one-tailed null due to an observed chi-square value of 19.60 which is greater than the one-tailed 5.0% critical chi-square
d. Yes, reject this one-tailed null due to an observed chi-square value of 27.44 which is greater than the one-tailed 5.0% critical chi-square

406.2. Your analysis of an asset price series determines the price follows a lognormal distribution with parameters values of mu (μ) = 3.4 and sigma (σ) = 1.0. For example, the expected mean price = exp(μ + σ^2/2) = exp(3.4^2 + 1^2/2) = \$49.40. We want to specify the price level that will be exceeded with 50.0% probability; i.e., at approximately which price quantile (level) will the price exceed with 50% probability, and therefore also be lower than 50% of the time?

a. 30.0
b. 37.9
c. 49.4
d. 51.0

406.3. Over the last ten (n = 10) trading days, the daily volatility of two series are 5.0% and 3.0%. If the null hypothesis is that the series (samples) are drawn from the normal population, can we reject the null hypothesis and conclude these volatilities are statistically different with a confidence level of 95.0%? Please use this F distribution lookup table:
https://www.bionicturtle.com/images/2014/dailypq/406_3_f_lookup.png.

a. No, fail to reject null given observed F ratio of 1.67 and a higher critical F
b. No, fail to reject null given observed F ratio of 2.78 and a higher critical F
c. Yes, reject null given observed F ratio of 1.67 and a lower critical F
d. Yes, reject null given observed F ratio of 2.50 and a lower critical F

#### Bias

##### New Member
406.1. = d
Ho=<0.01 vs Ha>0.01 - one tailed test
X^2 at 14 df and 5% critical value is 23.68. So, reject Ho if chi-squared statistics is > 23.68 critical value.
X^2 statistics = (Q^2/Q0^2)*(n-1)df=0. =(0.0196/0.01)*14=27.44
Thus, chi-squared statistics 27.44 is greater than 23.68 and Ho is rejected.

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