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CFA Level 1
Quantitative Methods

Determining P-value from T-test

Hard Hypothesis Testing P-values And Significance

A financial analyst is testing whether a new trading strategy can outperform the market average return of 8% per annum. She collects a sample of 30 monthly returns from the strategy over the last three years and calculates the average return for the sample to be 10% with a standard deviation of 2%. Assuming the returns are normally distributed, she sets up the following hypotheses:

Null Hypothesis (H0): The average return of the strategy is equal to the market average (μ = 8%)

Alternative Hypothesis (H1): The average return of the strategy is greater than the market average (μ > 8%)

The analyst calculates the test statistic using the formula for a one-sample t-test:

Test Statistic (t): $$t = \frac{\bar{x} - \mu}{s/\sqrt{n}}$$

Where:
$$\bar{x}$$ = Sample mean
$$\mu$$ = Population mean
$$s$$ = Sample standard deviation
$$n$$ = Sample size
After performing the calculations, she finds that the test statistic t is equal to 3.87. What is the P-value for this test statistic based on a one-tailed t-distribution with 29 degrees of freedom?

Hint

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