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

Answer:

a) $t_{\alpha}= 1.753$

b) $t_{\alpha}= -1.383$

c) $t_{\alpha/2}= \pm 2.179$

Step-by-step 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:

$t_{\alpha/2}= \pm 2.179$