Question

state whether the standardized test statistic t indicates that you should reject the null hypothesis. explain.
(a) ( t = 1.556 )
(b) ( t = 0 )
(c) ( t = 1.492 )
(d) ( t = - 1.567 )
(a) for ( t = 1.556 ), should you reject or fail to reject the null hypothesis?
a. reject ( h_0 ), because ( t < 1.528 ).
b. reject ( h_0 ), because ( t > 1.528 ).
c. fail to reject ( h_0 ), because ( t > 1.528 ).
d. fail to reject ( h_0 ), because ( t < 1.528 ).

Explanation:

Step1: Recall the rejection rule

In a one - tailed t - test, if the test statistic \(t\) is in the rejection region (i.e., \(t>t_{0}\) for a right - tailed test, where \(t_{0}\) is the critical value), we reject the null hypothesis \(H_{0}\). Here, the critical value \(t_{0}=1.528\) (right - tailed test as the rejection region is on the right side of the t - distribution curve).

Step2: Compare the test statistic with the critical value

For \(t = 1.556\), since \(1.556>1.528\) (i.e., the test statistic \(t = 1.556\) falls in the rejection region).

Answer:

B. Reject \(H_{0}\), because \(t>1.528\)