CFA® Level 1: Hypothesis Testing in Statistics

Calculating the P-value for a Sample Mean Test

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Question

A researcher has a sample of 900 observations from a population whose standard deviation is known to be 3,381. The mean of the sample is calculated to be

465.2. The null hypothesis is stated as Ho: mean < 200. The p-value in this case equals ________.

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A. B. C. D.

D

To test the hypothesis, you need to calculate the smallest z-statistic since the null hypothesis is unidirectional and to the left. This makes it the hardest to reject the null and you should always use the most stringent criterion for rejecting the null. After all, the null is the hypothesis maintained to be true by default and only a sufficient weight of evidence should be used to reject that view. The smallest z-statistic under the null is calculated to be (465.2 - 200)/(3381/(900^.5)) = 2.35. The right-tailed probability of observing a z-statistic which is at least as big as 2.35 equals 1.0 - 0.9906 = 0.0094 = 0.94%. This is the p-value of the right-tailed test in this sample.

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