Question

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 10 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 = 0.01 \\) level of significance based on a sample size of \\( n = 14 \\). click here to view the t-distribution area in right tail. (a) \\( t_{\alpha}= \\) (round to three decimal places as needed.) (b) \\( t_{\alpha}= \\) (round to three decimal places as needed.) (c) \\( t_{\frac{\alpha}{2}}= \\) (round to three decimal places as needed.)

Explanation:

Step1: Recall the t - distribution table usage

For a right - tailed test with degrees of freedom \(df = 10\) and \(\alpha=0.10\), we look up the value in the t - distribution table.

Step2: Locate the value

In the t - distribution table, for \(df = 10\) and right - tailed \(\alpha = 0.10\), the critical value \(t_{\alpha}\) is \(1.372\).

Answer:

(a) \(1.372\)