Question

the critical value and rejection region for the type of t - test with level of significance α and sample size n.

• tailed test, α = 0.05, n = 33

a. ( t_0=-1.692 ); ( t < - 1.692 )
b. ( t_0=-2.738 ); ( t < - 2.738 )
c. ( t_0 = 1.694 ); ( t>1.694 )
d. ( t_0=-1.694 ); ( t < - 1.694 )

Explanation:

Step1: Calculate degrees of freedom

Degrees of freedom \(df=n - 1\). Given \(n = 33\), so \(df=33-1 = 32\).

Step2: Find critical value

For a left - tailed \(t\) - test with \(\alpha=0.05\) and \(df = 32\). Using a \(t\) - distribution table or calculator, the critical value \(t_0\) is approximately \(-1.694\).

Step3: Determine rejection region

For a left - tailed test, the rejection region is \(t

Answer:

D. \(t_0=-1.694;t < - 1.694\)