### CFA Practice Question

Here are some cumulative probabilities for the chi-sqd distribution:

prob(chi-sqd15 > 32.80132) = 0.005
prob(chi-sqd15 > 30.57791) = 0.010
prob(chi-sqd15 > 27.48839) = 0.025
prob(chi-sqd15 > 24.99579) = 0.050

For a normally distributed random variable you wish to test the null hypothesis that the variance equals 25. The sample size is 16. The threshold value of the sample variance above which the null hypothesis will be rejected at the 5% level of significance is:
A. 41.66
B. 45.81
C. 6.77
Explanation: Remember the Null Hypothesis is that the variance is 'equal to'. This means the test is 2-tailed, so the right tail needs to have probability mass 2.5% (not 5%).

### User Contributed Comments6

User Comment
jsubhen Tricky. One needs to use the test statistic to find the sample variance. 15s(squared)/25 = 27.488
jpducros What does the 15 means in "chi-sqd15" ?
agolf88 15 degrees of freedom
lisab0131 Need to solve for the sample variance at which point you would reject the null hypothesis, in this case when the test statistic is above 27.48. so just work backwords: 27.48 = 15*S^2/(25) therefore at a s^2 above 45.81, you will reject
birdperson FYI, the test statistic is (N-1)(sample standard deviation/hypothesized standard deviation)
fobucina ^ Test Statistic is (N-1)(Sample Variance/Hypothesized Variance)
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