Question

state whether the standardized test statistic t indicates that you should reject the null hypothesis. explain.
(a) t = 2.052
(b) t = 0
(c) t = 1.977
(d) t = -2.088
(a) for t = 2.052, should you reject or fail to reject the null hypothesis?
a. reject ( h_0 ), because t < 2.033.
b. fail to reject ( h_0 ), because t < 2.033.
c. reject ( h_0 ), because t > 2.033.
d. fail to reject ( h_0 ), because t > 2.033.

Explanation:

Step1: Understand the rejection rule

In a one - tailed t - test, if the test statistic \(t\) is greater than the critical value \(t_0\), we reject the null hypothesis \(H_0\). Here, the critical value \(t_0 = 2.033\).

Step2: Compare the test statistic and the critical value

For \(t = 2.052\), we check the relationship between \(t\) and \(t_0\). Since \(2.052>2.033\) (i.e., \(t > t_0\)).

Answer:

C. Reject \(H_0\), because \(t>2.033\)