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. fail to 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. reject ( h_0 ), because ( t < 2.033 ).
(d) for ( t = - 2.088 ), should you reject or fail to reject the null hypothesis?
a. reject ( h_0 ), because ( t > 2.033 ).
b. reject ( h_0 ), because ( t < 2.033 ).
c. fail to 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 (right - tailed in this case as the critical region is on the right side), we reject the null hypothesis \(H_0\) if the test statistic \(t\) is greater than the critical value \(t_0\). The critical value \(t_0 = 2.033\).

Step2: Analyze each value of \(t\)

• For \(t = 2.052\):

Since \(2.052>2.033\), we reject \(H_0\) because the test statistic \(t\) falls in the rejection region.

• For \(t = 0\):

Since \(0<2.033\), we fail to reject \(H_0\) because the test statistic \(t\) does not fall in the rejection region.

• For \(t = 1.977\):

Since \(1.977<2.033\), we fail to reject \(H_0\) because the test statistic \(t\) does not fall in the rejection region.

• For \(t=-2.088\):

In a right - tailed test, negative values of \(t\) are even further from the rejection region (which is on the positive side). Since \(- 2.088<2.033\), we fail to reject \(H_0\)

Answer:

(a) C. Reject \(H_0\), because \(t > 2.033\)
(b) A. Fail to reject \(H_0\), because \(t<2.033\)
(c) A. Fail to reject \(H_0\), because \(t<2.033\)
(d) C. Fail to reject \(H_0\), because \(t<2.033\)