Respuesta :
Answer:
(a) The critical value of t at P = 0.01 and 15 degrees of freedom is 2.602.
(b) The critical value of t at P = 0.05 and 19 degrees of freedom is -1.729.
(c) The critical value of t at P = 0.025 and 12 degrees of freedom is -2.179 and 2.179.
Step-by-step explanation:
We have to find the critical t values for each of the following levels of significance and sample sizes given below.
As we know that in the t table there are two columns. The horizontal column is represented by the symbol P which represents the level of significance and the vertical column is represented by the symbol '[tex]\nu[/tex]' which represents the degrees of freedom.
(a) A right-tailed test of a population mean at the α=0.01 level of significance with 15 degrees of freedom.
So, here the level of significance = 0.01
And the degrees of freedom = n - 1 = 15
Now, in the t table, the critical value of t at P = 0.01 and 15 degrees of freedom is 2.602.
(b) A left-tailed test of a population mean at the α=0.05 level of significance with a sample size of n = 20.
So, here the level of significance = 0.05
And the degrees of freedom = n - 1
= 20 - 1 = 19
Now, in the t table, the critical value of t at P = 0.05 and 19 degrees of freedom is -1.729.
(c) A two-tailed test of a population mean at the α=0.05 level of significance with a sample size of n = 13.
So, here the level of significance = [tex]\frac{0.05}{2}[/tex] = 0.025 {for the two-tailed test}
And the degrees of freedom = n - 1
= 13 - 1 = 12
Now, in the t table, the critical value of t at P = 0.025 and 12 degrees of freedom is -2.179 and 2.179.
