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. 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 ).

(b) for ( t = 0 ), should you reject or fail to reject the null hypothesis?
a. reject ( h_0 ), because ( t > 1.528 ).
b. fail to reject ( h_0 ), because ( t > 1.528 ).
c. fail to reject ( h_0 ), because ( t < 1.528 ).
d. reject ( h_0 ), because ( t < 1.528 ).

Explanation:

Step1: Understand the rejection rule

In a one - tailed t - test (right - tailed in this case as the critical region is on the right side), if the calculated t - statistic \(t\) is greater than the critical value \(t_{\alpha}\) (here \(t_{\alpha}=1.528\)), we reject the null hypothesis \(H_{0}\). If \(t\leq t_{\alpha}\), we fail to reject the null hypothesis.

Step2: Analyze each value of \(t\)

• For \(t = 1.556\):

Since \(1.556>1.528\), we reject \(H_{0}\) (because \(t>1.528\)).

• For \(t = 0\):

Since \(0<1.528\), we fail to reject \(H_{0}\) (because \(t < 1.528\)).

• For \(t=1.492\):

Since \(1.492<1.528\), we fail to reject \(H_{0}\) (because \(t < 1.528\)).

• For \(t=-1.567\):

In a right - tailed test, negative \(t\) - values are even more in the non - rejection region (far from the critical region on the right). So we fail to reject \(H_{0}\) (because \(t < 1.528\)).

Answer:

(a) B. Reject \(H_{0}\), because \(t>1.528\).
(b) C. Fail to reject \(H_{0}\), because \(t < 1.528\).
(c) D. Fail to reject \(H_{0}\), because \(t < 1.528\).
(d) D. Fail to reject \(H_{0}\), because \(t < 1.528\).