CFA Level I · CFA Level I Exam · Estimation and Hypothesis Testing
An analyst estimates a sample correlation of 0.40 between two asset returns using 27 paired observations and tests the null hypothesis that the population correlation is zero. The calculated t-statistic and the most likely conclusion at the 5% significance level (two-tailed critical value of 2.060 for 25 degrees of freedom) are:
The t-statistic is 2.18, which exceeds the critical value of 2.060, so the analyst rejects the null hypothesis of zero correlation. It is computed as 0.40 times the square root of 25 divided by the square root of 0.84.
- At = 2.18; fail to reject the null hypothesis
- Bt = 2.18; reject the null hypothesisCorrect
- Ct = 2.18 is not valid because the correlation must exceed 0.5; reject the null hypothesis
Explanation
t = r√(n-2)/√(1-r²) = 0.40×√25/√0.84 = 2.0/0.9165 = 2.18. This exceeds 2.060, so the null of zero correlation is rejected. The third option invents a requirement and is incorrect.
Did you get it right without looking?
One question tells you little. A timed set on Estimation and Hypothesis Testing shows your real accuracy, how long you take and where you lose marks.
More Estimation and Hypothesis Testing questions
- The standard deviation of a sample of 49 daily returns is 2.8%. The population standard deviation is unknown. The estimated standard error o…
- A portfolio manager divides a bond universe into 4 groups by credit rating and then draws a random sample from each group in proportion to t…
- Compared with the bootstrap, the jackknife is most accurately described as:
- Which of the following is the most likely reason an analyst would choose a nonparametric test rather than a parametric test?
- An analyst draws large random samples from a population that is clearly non-normal with a finite variance. According to the central limit th…
- An analyst wants to test whether the mean monthly return of a fund differs from zero, using 36 monthly observations. The population variance…