Question

a) Determine the critical value(s) for a right-tailed test of a population mean at the a =0.10 level of significance with 15 degrees of freedom
b) Determine the critical value(s) for a left-tailed test of a population mean at the a=0.10 level of significance based on a sample size of n=10
c)Determine the critical value(s) for a two-tailed test of a population mean at the a=0.01 level of significance based on a sample size of n=13

Answer 1

Answer:

a) $df = n-1= 15-1= 14$

The value of $\alpha=0.1$ and  we are conducting a right tailed test, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=T.INV(1-0.1,14)".And we see that

$t_{\alpha/2}=1.345$

b)$df = n-1= 10-1= 9$

The value of $\alpha=0.1$ and  we are conducting a left tailed test, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=T.INV(0.1,9)".And we see that

$t_{\alpha/2}=-1.383$

c) $df = n-1= 13-1= 12$

The value of $\alpha=0.01$ and  we are conducting a two tailed test, the value of $\alpha/2 = 0.005$, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,12)".And we see that

$t_{\alpha/2}=\pm 3.505$

Step-by-step explanation:

Part a

We need to find the degrees of freedom given by:

$df = n-1= 15-1= 14$

The value of $\alpha=0.1$ and  we are conducting a right tailed test, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=T.INV(1-0.1,14)".And we see that

$t_{\alpha/2}=1.345$

Part b

We need to find the degrees of freedom given by:

$df = n-1= 10-1= 9$

The value of $\alpha=0.1$ and  we are conducting a left tailed test, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=T.INV(0.1,9)".And we see that

$t_{\alpha/2}=-1.383$

Part c

We need to find the degrees of freedom given by:

$df = n-1= 13-1= 12$

The value of $\alpha=0.01$ and  we are conducting a two tailed test, the value of $\alpha/2 = 0.005$, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,12)".And we see that

$t_{\alpha/2}=\pm 3.505$