Sample Mean and Hypothesis Testing in CFA® Level 1 Exam - Test Prep

Sample Mean and Hypothesis Testing

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Question

A researcher has a sample of 700 observations from a population whose standard deviation is known to be 1,235.6. The mean of the sample is calculated to be

219.2. The null hypothesis is stated as Ho: mean = 150 and the alternative is non-directional. The p-value in this case equals ________.

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Explanations

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A. B. C. D.

Explanation

The z-statistic under the null equals (219.2 - 150)/(1235.6/(700^.5)) = 1.48. Since the alternative is non-directional, you must use a two-tailed test and ask the question, "What is the probability of observing a z-statistic at least as large in magnitude as 1.48?" The answer to this will give you the p- value for this sample under the two-tailed test. The right-tailed probability of observing a z-statistic which is at least as big as 1.48 equals 1.0 - 0.9306 = 0.0694 = 6.94%. The left-tailed probability of observing a z-statistic which is at least as small as - 1.48 also equals 6.94% since the standard normal distribution is symmetrical about zero.

Therefore, the p-value of this two-tailed test in this sample equals 6.94%*2 = 13.88%.

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