Question

find the critical value and rejection region for the type of t - test with level of significance α and sample size n.
right - tailed test, α = 0.01, n = 23
a. ( t_0=-2.508 ); ( t<-2.508 )
b. ( t_0 = 2.500 ); ( t>2.500 )
c. ( t_0=2.508 ); ( t>2.508 )
d. ( t_0=1.321 ); ( t>1.321 )

Explanation:

Step1: Calculate degrees of freedom

Degrees of freedom \(df=n - 1\). Given \(n = 23\), so \(df=23-1 = 22\).

Step2: Find critical value using t - distribution table

For a right - tailed test with \(\alpha=0.01\) and \(df = 22\), looking up the t - distribution table, the critical value \(t_0\) is \(2.508\).

Step3: Determine rejection region

For a right - tailed test, the rejection region is \(t>t_0\), so \(t > 2.508\).

Answer:

C. \(t_0 = 2.508\); \(t>2.508\)