exhibit 8 of the current CFA curriculum states 2 methods for decision making.
I) comparing the calcluated test statistic with the critical value.
II) comparing the calculated test statistic with the bounds of the confidence interval.
calculating the test statistic requires sample mean, hypothesized value, variance and sample size
getting the critical value needs a level of confidence and finally, calculating the confidence intervals bounds requires the sample mean, critical value, variance and sample size.
Overall, the same figures are needed in both methods. So which method do I need to use?
Intuitively, I would never use the 2nd method, as it is more effort. (1 additional step).
Greetings friend! If you are asking about the CFA exam and their questions about statistical significance, for my 2 cents you should be prepared to use any method, keep all your mental tools sharp for exam day. They may give you enough information to answer a question using one approach but not another approach.
For example on a mock question you may find that they do not give you all the data you mention above to calculate the confidence interval, but they instead give you the significance value and the p-value, so they want to see if you can make a decision based on that sort of thing. Or they may give you the confidence interval and the p-value but not the sample mean or variance.
If they give you all the data you mention above to compare the test statistic to the critical value, then that sometimes the fastest way to solve the problem but usually it’s slower than comparing the p-value to the significance value if they give you that data too (remember that a confidence interval = 1- significance value, so if they give you the confidence interval you can quickly calculate what the significance level is and compare it to the p-value).
This is a long way of saying that you should be prepared for anything, and there are ways for the exam writers to selectively provide data that allows you to solve a problem in one way but maybe not in both ways, if they want to be tricky. If they give you enough data to solve it in your preferred way, go for it of course.
Cheers - good luck - you got this
Hi - thank you for your detailed answer.
My point was that if I need to calculate the test statistic, I have all figures to also calculate either the confidence interval od get the critical value,
because the sample mean, the hypothesized value and the (sample) variance as well as the sample size need to be given in order to calculate the test statistic?
So, I can decide whether to use the critical value approach or to calculate the confidence interval?
Greetings again friend! In general for the CFA exams, if you find situations where you see that you have all the information required to solve a problem in multiple ways, then definitely feel free to use the fastest method you’re most comfortable with. Cheers - good luck - you got this