Complete parts (a) through (c) below. (a) Determine the critical value(s) for a right-tailed test of a population mean at the alpha = 0.10 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 = 0.01 level of significance based on a sample size of n = 20.

(c) Determine the critical value(s) for a two-tailed test of a population mean at the alpha = 0.05 level of significance based on a sample size of n = 14.

(a) 1.341

(b) -2.539

(c) -2.160 and 2.160

Step-by-step explanation:

(a) We have to find the critical value(s) for a right-tailed test of a population mean at the alpha = 0.10 level of significance with 15 degrees of freedom.

Since the degrees of freedom are included here, so we will use t table here for a population mean test.

In the table there are two values given, one is the degrees of freedom and another is the value of P.

P is the level of significance at which the critical values are calculated.

So, here the degrees of freedom (n - 1) = 15 and the level of significance for a right-tailed test is 0.10, i.e. P = 10%

Now, looking in the t table with P = 10% and = 15, we get the critical value of 1.341.

(b) We have to find the critical value(s) for a left-tailed test of a population mean at the alpha = 0.01 based on a sample size of n = 20.

Since the degrees of freedom are included here, so we will use t table here for a population mean test.

In the table there are two values given, one is the degrees of freedom and another is the value of P.

P is the level of significance at which the critical values are calculated.

So, here the degrees of freedom (n - 1) = 20 - 1 = 19 and the level of significance for a left-tailed test is 0.01, i.e. P = 1%

Now, looking in the t table with P = 1% and = 19, we get the critical value of 2.539. But since it is a left-tailed test, so the critical value will be -2.539.

(c) We have to find the critical value(s) for a two-tailed test of a population mean at the alpha = 0.05 level of significance based on a sample size of n = 14.

Since the degrees of freedom are included here, so we will use t table here for a population mean test.

In the table there are two values given, one is the degrees of freedom and another is the value of P.

P is the level of significance at which the critical values are calculated.

So, here the degrees of freedom (n - 1) = 14 - 1 = 13 and the level of significance for a two-tailed test is is 0.025, i.e. P = 2.5%.

Now, looking in the t table with P = 2.5% and = 13, we get the critical value of -2.160 and 2.160 for a two-tailed test.

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