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.

a)

b)

c)

Step-by-step explanation:

Part a

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

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:

Part b

For this case the significance is the degrees of freedom are:

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

Part c

For this case the significance is and the degrees of freedom are:

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

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step-by-step explanation: