Guys how do we know the probability is one tailed or two. Like the one in the following question. Thanks. Ken Wallace is interested in testing whether the average price to earnings (P/E) of firms in the retail industry is 25. Using a t-distributed test statistic and a 5% level of significance, the critical values for a sample of 40 firms is/are: A) -2.023 and 2.023. B) -1.685 and 1.685. C) -1.96 and 1.96. D) 1.685. The correct answer was A. There are 40-1=39 degrees of freedom and the test is two-tailed. Therefore, the critical t-values are ± 2.023. The value 2.023 is the critical value for a one-tailed probability of 2.5%.
When you are checking for equality (eg P/E is 25) you use a two tailed test , else (eg if you were checking P/E > 25 or P/E < 25) you would use a one tailed test.
When the Null Hypothesis has an equal to sign and the alternative hypothesis has a ‘not-equal-to’ sign, you have to use 2-tailed test. Thats because the actual value can be less than or greater than the hypothised value. in your question , H0 is : avg P/E = 25 Ha is : avg P/E not equal to 25. So you use 2 tailed. You use 1-tailed when there is a ‘less than’ or ‘greater than’ sign in your hypothesis.
Is it that simple! Thanks SV102307
Alternative Hypothesis cannot have equality sign. Only null hypothesis can. So, Ho :Mu = Mu0, Mu <= Mu0 , Mu >= Mu0 are stated as null hypthesis, and you try to find evidence that can reject/fail to reject null hypothesis by checkcing the alternative hypothesis.
One tip for everybody: If you want to know how to construct hypothesis / number of tails, always remember the following. What you want to show, put that in H1. If you want to show µ>c then thats your H1. If you want to show µc then thats your H1. And remember: you can’t show /proof with a test equality µ=c. You can only show inquality. CFAisok