CFA Level I · CFA Level I Exam · Estimation and Hypothesis Testing
An analyst tests H0: μ = 5.0% against Ha: μ ≠ 5.0% using 64 annual returns. The sample mean is 6.2% and the sample standard deviation is 6.0%. The population variance is unknown. The calculated test statistic and the decision at the 5% level (critical t-value about ±2.00 with 63 degrees of freedom) are most likely:
The test statistic is 1.60, found as (6.2% − 5.0%) divided by a standard error of 0.75% (6.0% over the square root of 64). It lies within ±2.00, so the analyst fails to reject the null hypothesis.
- A1.60; fail to reject H0Correct
- B1.60; reject H0
- C9.60; reject H0
Explanation
Standard error = 6.0/√64 = 6.0/8 = 0.75. The t-statistic = (6.2 − 5.0)/0.75 = 1.60. Because 1.60 lies inside ±2.00, the null is not rejected. The 9.60 distractor results from dividing by 0.125 instead of 0.75 (a wrong standard error).
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