Quiz: Statistical Analysis

The t-Test

Let's say we've calculated a set of monthly returns, and we've calculated their mean, \bar{x} . Now, we'll perform a t-test to see if we can infer from our limited data set that our trading strategy is likely to yield positive returns. We'll perform a one-tailed t-test with the null hypothesis that \mu , the true mean return from our trading strategy, equals 0.

In which situation might we conclude that our trading strategy is likely to yield positive returns (check all that apply)?

\bar{x} = 0.2%; null hypothesis \mu = 0; alternative hypothesis \mu > 0; p = 0.0049

\bar{x} = 6%; null hypothesis \mu = 0; alternative hypothesis \mu > 0; p = 0.5

\bar{x} = 2%; null hypothesis \mu = 0; alternative hypothesis \mu > 0; p = 0.15

\bar{x} = 4%; null hypothesis \mu = 0; alternative hypothesis \mu > 0; p = 0.034

\bar{x} = –0.5%; null hypothesis \mu = 0; alternative hypothesis \mu < 0; p = 0.046

SOLUTION:

\bar{x} = 0.2%; null hypothesis \mu = 0; alternative hypothesis \mu > 0; p = 0.0049
\bar{x} = 4%; null hypothesis \mu = 0; alternative hypothesis \mu > 0; p = 0.034

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