CFA Practice Question
Matthew Eagleburger is testing the following hypotheses:H0: μ = 12 versus Ha: μ ≠ 12
His sample of 19 observations has yielded a mean of 10.8 and a standard deviation of 6.55. Can Matthew reject the null hypothesis on the basis of a 95% confidence level? What is the critical test statistic?
A. Yes; 1.734
B. No; 1.734
C. No; 2.101
Explanation: Due to the small sample size we use the t-test. Based on 95% probability for a two-tailed test, the critical t-value for 18 (=19 - 1) degrees of freedom is 2.101. The test statistic is:t = (10.8 - 12.0)/(6.55/191/2) = -0.80
As the absolute value of the test statistic is less than the critical t-value, Matthew cannot reject the null hypothesis.
User Contributed Comments 13
| User | Comment |
|---|---|
| danlan | The critical test value is not the calculated value, but the one on t table. |
| danlan | It should be greater than the corresponding value for z-test which is 1.96, so only value 2.101 is possible critical test-statistic (not 1.734) |
| jayjunk | Actually as it is a two sided test (not equal to), the critical Z value is 2.56, not 1.96. |
| jharris | On a two-sided 99% z-value is 2.56, 95% is 1.96 |
| labsbamb | but if u don`t have the T-table, how we can find the t-critical ? |
| dimanyc | Since you should know your 50%, 68% 90%, 95% and 99% z values by heart, you would notice that Z (95%) = 1.96%. T-value for the same critical value is always more than z and the smaller the n is, the further the distance. |
| achu | Athough some of us know these "main" %iles by memory, I am confident that on a real exam we'd be given the values or a table subset. |
| ontrack | anybody here who has given level 1 before and can confirm if we do get the tables in the exam? |
| deibertm | They will provide the t or z value. If not they give you a small table with only about 5 to 10 cells to pick from. I would not be concerned with this. They will expect you to know a z of 1.96 and 1.68 though |
| Booster | Gone thru the material before but solving questions is a new ball game. anyone experienced this as well? |
| SuperKnight | This one gave me a headache, I didn't see the "critical" word there, so when I kept getting -0.80, and didn't see it as a test statistic I thought I didn't have a clue what I was doing at all. Makes sense now, gotta watch the wording. I don't think you need the tables on this one. If you remember that the Z-statistic for 95% is 1.96, and you know that the t-statistic has to be larger, then you know it can't be 1.734. |
| Oksanata | i've taken an exam before and i can confirm that they will not give z-values for those you must know by heart. like for 68%, 90%, 95%, 99%. for all others, especially for t-distribution they will give it..that's why i was surprised by this question as they are not giving the fragment of t-table here... |
| mrpman | hey can someone tell me these values, to my understanding for a normal distribution 68% of returns lie within 1 standard deviation (std), 90% lie within 1.65 std, 95% lie within 1.96 std, and 99% lie within 2.68 std... please correct me if i am wrong |