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) 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: Determine the rejection region

In a two - tailed t - test, the null hypothesis \(H_0\) is rejected if \(t < -t_0\) or \(t>t_0\), where \(t_0 = 1.456\)

Step2: Compare the test statistic with the critical values

For \(t=-1.471\), we compare \(-1.471\) with \(-t_0=-1.456\)
Since \(-1.471<-1.456\)

Answer:

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