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# P1.T2.315. Miller's hypothesis tests, continued

#### Nicole Seaman

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AIMs: Describe the process of selecting and constructing a null hypothesis. Interpret the results of hypothesis tests with a specific level of confidence. Describe and apply the principle of Chebyshev’s inequality

Questions:

315.1. Roger collects a set of 61 daily returns over a calendar quarter for the stock of XYZ corporation. He computes the sample's daily standard deviation, which is annualized in order to generate a sample volatility of 27.0%. His null hypothesis is that the true (population) volatility is 30.0%. Can he reject the null with 95% confidence?

a. No, the test statistic is 1.59
b. No, the test statistic is 48.60
c. Yes, the test statistic is 24.03
d. Yes, the test statistic is 72.57

315.2. A fund of funds has investments in 36 hedge funds. At the end of the year, the mean return of the constituent hedge funds was 13.0%. The standard deviation of the funds' returns was 9.0%. The benchmark return for the fund of funds was 10.0%. With 95.0% confidence, can we accept the one-sided alternative hypothesis that the fund of funds exceeded its benchmark; i.e., can we reject the one-sided null hypothesis that the fund of funds' true performance is less than or equal to 10.0%? (note: variation on Miller's Question 5.2)

a. Yes, true fund performance is greater than 10.0% as computed t-stat of 2.00 exceeds lookup value of 1.690
b. Yes, true fund performance is greater than 10.0% as computed t-stat of 2.00 does not exceed lookup value of 2.030
c. No, true fund performance is not greater than 10.0% as computed t-stat of 2.00 exceeds lookup value of 1.690
d. No, true fund performance is not greater than 10.0% as computed t-stat of 2.00 does not exceed lookup value of 2.030

315.3. Among a sample of annual fund returns, the mean is 11.0% with standard deviation of 2.0%. According to Chebyshev’s inequality, what percentage of returns fall within 6.0% and 16.0%?

a. At least 60%
b. At most 60%
c. At least 84%
d. At most 84%