Please I want to understand the rationale behind our failure to reject (Ho) because our T-stat and T-critical both have zero among their numbers ; but if T-critical value have non-zero number in its value, and T-stat does have zero among its number, we reject Ho , and thus conclude that the independent variable significantly impacted on the dependent variable.
Why based our acceptance/rejection decision on the presence of Zero in the T-critical value?
Thank you.
S2000 to the rescue - this is in his Level 1 material
http://financialexamhelp123.com/cfa-level-i/
Look for the set of readings on Hypothesis testing
I think this is the example you are looking for
Cpk123, you din’t seems to read my question carefully, i asked a question, and you have not provided any solution to it.
I read in the Level 2 Quant material that we reject Ho if the Critical value has zero (0), and our T-stat also contains Zero (0). All i want to know is the rational behind that decision.\
Thanks.
What do you mean with “the critical value has zero (0)”?. The critical value is a specific value like 1.45 or 1.69
Also, the T-stat is a specific value, like 1.11 or 2.22 or 1.8975, so what you mean with the zero case.
I can note that you may be confusing this with the confidence interval, where if a CI contains the zero (0) within it, then we fail to reject the Ho. This is how they are linked (CI and hypothesis testing).
Does this help?
Oh sorry, you already meant the confidence interval case.
If you go Schweser’s book1, Reading 11, LOS e (pag 318) you will see how CI and hypothesis testing are linked.
If you have a confidence interval for beta(i) as:
A— (-2.5,+3.1) you can see that the possible range of values for beta(i) is from negative 2.5 to positive 3.1-- this interval contains zero-- you do not have evidence to conclude that beta(i) has a true value different from zero (or any other number in the interval). In other words, you have insufficient evidence to conclude that variable (i) has a relationship with the DV. This is equivalent to doing a hypothesis test (Ho: Beta(i)=0) and generating a test statistic with an absolute value that is less than the (positive) critical value (say alpha 0.05, -1.96 < calculated test statistic < 1.96).
B-- (+2, +6) again, the possible range of values for beta(i) is between positive 2 and positive 6-- this interval doesn’t contain zero. Therefore, we can conclude that the true value of beta (i) is different from zero (the variable has statistical utility to predict the DV). This is equivalent to doing a hypothesis test and seeing that the calculated test statistic is greater than 1.96 (again for alpha = 0.05, 2 tailed test).
The critical values used in the calculation of a confidence interval are the same critical values used in a rejection region (2-tailed test, same significance level). Overall, confidence intervals are more informative, as they give you a range of possible values of the true parameter. A p-value only tells you the probability that you’re wrong without any indication of the practical significance of the results (in this case, how large the slope might be).
Edit: I want to clarify one more thing that you said in your first post, OP. The confidence interval is a range of possible values for the parameter of interest (population mean, population slope, etc.). It is not a bunch of critical values (as it seems you might have thought). Also (for another example), if I wanted to test that the true slope, beta (i), was not equal to 1-- a confidence interval containing 1 (0.5 to 7.0, for example) would be equivalent to a hypothesis test where Ho: beta(i) = 1, Ha: beta(i) not equal to 1,and we FTR Ho. Confidence intervals and tests of hypothesis will lead you to the same conclusion regarding statistical significance (for reasons mentioned before about the calculations and decision rules).
I hope this helps clarify how they’re related.
Thank you Harrogath and Tickersu…