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. reject h0, because t < 2.033.
b. fail to reject h0, because t < 2.033.
c. reject h0, because t > 2.033.
d. fail to reject h0, because t > 2.033.

(b) for t = 0, should you reject or fail to reject the null hypothesis?
a. fail to reject h0, because t > 2.033.
b. reject h0, because t > 2.033.
c. reject h0, because t < 2.033.
d. fail to reject h0, because t < 2.033.

Explanation:

Step1: Recall the rejection rule for one - tailed t - test

In a right - tailed t - test, if the test statistic \(t\) is greater than the critical value \(t_0\), we reject the null hypothesis \(H_0\). If \(t\leq t_0\), we fail to reject \(H_0\). Here, \(t_0 = 2.033\)

Step2: Analyze each value of \(t\)

• For \(t = 2.052\):

Since \(2.052>2.033\), we reject \(H_0\)

• For \(t = 0\):

Since \(0<2.033\), we fail to reject \(H_0\)

• For \(t = 1.977\):

Since \(1.977<2.033\), we fail to reject \(H_0\)

• For \(t=-2.088\):

In a right - tailed test, negative values of \(t\) are even more in the non - rejection region (because the critical region is on the right side). So we fail to reject \(H_0\)

Answer:

(a) Reject \(H_0\), because \(t = 2.052>2.033\)
(b) Fail to reject \(H_0\), because \(t = 0<2.033\)
(c) Fail to reject \(H_0\), because \(t = 1.977<2.033\)
(d) Fail to reject \(H_0\), because \(t=-2.088<2.033\) (in a right - tailed test, negative \(t\) values are not in the rejection region)