Question

Complete parts ​(a) through ​(c) below.

​(a) Determine the critical​ value(s) for a​ right-tailed test of a population mean at the alpha equals0.10 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 alpha equals0.01 level of significance based on a sample size of nequals 20 .

​(c) Determine the critical​ value(s) for a​ two-tailed test of a population mean at the alpha equals0.05 level of significance based on a sample size of nequals 11.

Answer 1

a)
`t_(crit)= 1.34`

b)
`t_(crit)=-2.539`

c)
`t_(crit)=\pm 2.228`

Explanation:

Part a

The significance level given is
`\alpha=0.1` and the degrees of freedom are given by:

`df = n-1= 15`

Since we are conducting a right tailed test we need to find a critical value on the t distirbution who accumulates 0.1 of the area in the right and we got:

`t_(crit)= 1.34`

Part b

The significance level given is
`\alpha=0.01` and the degrees of freedom are given by:

`df = n-1= 20-1=19`

Since we are conducting a left tailed test we need to find a critical value on the t distirbution who accumulates 0.01 of the area in the left and we got:

`t_(crit)=-2.539`

Part c

The significance level given is
`\alpha=0.05` and
`\alpha/2 =0.025` and the degrees of freedom are given by:

`df = n-1= 11-1=10`

Since we are conducting a two tailed test we need to find a critical value on the t distirbution who accumulates 0.025 of the area on each tail and we got:

`t_(crit)=\pm 2.228`