Question

state whether the standardized test statistic t indicates that you should reject the null hypothesis. explain.
(a) ( t = - 1.471 )
(b) ( t = 1.404 )
(c) ( t = 1.533 )
(d) ( t = - 1.471 )
a. fail to reject ( h_0 ), because ( t < - 1.456 ).
b. reject ( h_0 ), because ( - 1.456 < t < 1.456 ).
c. fail to reject ( h_0 ), because ( t > 1.456 ).
d. reject ( h_0 ), because ( t > 1.456 ).
(d) for ( t = - 1.471 ), should you reject or fail to reject the null hypothesis?
a. fail to reject ( h_0 ), because ( t < - 1.456 ).
b. reject ( h_0 ), because ( t < - 1.456 ).
c. fail to reject ( h_0 ), because ( - 1.456 < t < 1.456 ).
d. reject ( h_0 ), because ( t > 1.456 ).

Explanation:

Step1: Recall the rejection rule

In a two - tailed t - test, we reject the null hypothesis \(H_0\) if \(t < -t_0\) or \(t>t_0\), where \(t_0 = 1.456\) (from the given critical values in the problem).

Step2: Analyze \(t=-1.471\)

We have \(t=-1.471\) and \(-t_0=-1.456\). Since \(-1.471<-1.456\) (i.e., \(t < -t_0\)).

Answer:

B. Reject \(H_0\), because \(t < - 1.456\).