Complete parts (a) through (c) below. (a) determine the critical value(s) for a right-tailed test of a population mean at the alphaequals0.10 level of significance with 20 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 nequals15. (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 nequals12. click here to view the t-distribution area in right tail.

a) The critical value on this case would be

b) The critical value on this case would be

c) The critical values on this case would be

Step-by-step explanation:

Part a

The system of hypothesis on this case would be:

Null hypothesis:

Alternative hypothesis:

Where is the value that we want to test.

In order to find the critical value we need to find first the degrees of freedom, on this case that is given df=20. Since its an upper tailed test we need to find a value a such that:

And we can use excel in order to find this value with this function: "=T.INV(0.9,20)". The 0.9 is because we have 0.9 of the area on the left tail and 0.1 on the right.

The critical value on this case would be

Part b

The system of hypothesis on this case would be:

Null hypothesis:

Alternative hypothesis:

Where is the value that we want to test.

In order to find the critical value we need to find first the degrees of freedom, given by:

Since its an lower tailed test we need to find b value a such that:

And we can use excel in order to find this value with this function: "=T.INV(0.1,14)". The 0.1 is because we have 0.1 of the area accumulated on the left of the distribution.

The critical value on this case would be

Part c

The system of hypothesis on this case would be:

Null hypothesis:

Alternative hypothesis:

Where is the value that we want to test.

In order to find the critical value we need to find first the degrees of freedom, given by:

Since its a two tailed test we need to find c value a such that:

or

And we can use excel in order to find this value with this function: "=T.INV(0.025,11)". The 0.025 is because we have 0.025 of the area on each tail.

The critical values on this case would be

i think is g(1)=-1.

hope that i can