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 = 32
a. t₀ = 2.449; t > 2.449
b. t₀ = - 2.453; t < - 2.453
c. t₀ = 1.309; t > 1.309
d. t₀ = 2.453; t > 2.453

Explanation:

Step1: Calculate the degrees of freedom

The degrees of freedom \(df=n - 1\). Given \(n = 32\), so \(df=32-1 = 31\).

Step2: Find the critical value

For a right - tailed \(t\) - test with \(\alpha=0.01\) and \(df = 31\), we look up the \(t\) - value in the \(t\) - distribution table. The critical value \(t_0\) is such that the area to the right of \(t_0\) under the \(t\) - distribution curve with \(df = 31\) is \(\alpha=0.01\). From the \(t\) - distribution table, \(t_0 = 2.453\).

Step3: Determine the rejection region

For a right - tailed test, the rejection region is \(t>t_0\). So the rejection region is \(t>2.453\).

Answer:

D. \(t_0 = 2.453;t>2.453\)