Question

determine the critical value for a left - tailed test of a population mean at the \\( \alpha = 0.1 \\) level of significance based on a sample size of \\( n = 22 \\). round to three decimal places

oa. \\( - 1.323 \\)
ob. 1.323
oc. \\( - 2.518 \\)
od. 1.321

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\). Given \(n = 22\), so \(df=22-1 = 21\).

Step2: Use the t - distribution table

For a left - tailed test with \(\alpha=0.1\) and \(df = 21\). Looking up the t - distribution table (or using a statistical software/ calculator with t - distribution function), the critical value \(t_{\alpha,df}\) for a left - tailed test is such that \(P(T<t_{\alpha,df})=\alpha\).
From the t - distribution table, when \(df = 21\) and \(\alpha = 0.1\), the critical value \(t=-1.323\) (negative for left - tailed test).

Answer:

A. - 1.323