Question

Complete parts ​(a) through ​(c) below. ​(a) Determine the critical​ value(s) for a​ right-tailed test of a population mean at the alphaequals0.05 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 alphaequals0.10 level of significance based on a sample size of nequals10. ​(c) Determine the critical​ value(s) for a​ two-tailed test of a population mean at the alphaequals0.05 level of significance based on a sample size of nequals13.

Answer 1

a)
`t_(\alpha)= 1.753`

b)
`t_(\alpha)= -1.383`

c)
`t_(\alpha/2)= \pm 2.179`

Explanation:

Part a

For this case we know that the degrees of freedom are:

`df = 15`

And we want a right tailed test so then we need to find in the t distribution with degrees of freedom =15 a critical value who accumulate 0.05 of the area in the right and we got:

`t_(\alpha)= 1.753`

Part b

For this case the significance is
`\alpha=0.1` the degrees of freedom are:

`df = n-1= 10-1=9`

And since is a left tailed test the critical value for this case would be:

`t_(\alpha)= -1.383`

Part c

For this case the significance is
`\alpha=0.05` and
`\alpha/2=0.025` the degrees of freedom are:

`df = n-1= 13-1=12`

And since is a two tailed test the critical values for this case would be:

`t_(\alpha/2)= \pm 2.179`