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 ) (d) for ( t = - 1.567 ), should you reject or fail to reject the null hypothesis?

Explanation:

Step1: Analyze the critical value

The critical value \(t_{0}=1.528\). In a one - tailed \(t\) - test (right - tailed as the shaded region is on the right), we reject \(H_{0}\) when \(t>t_{0}\) and fail to reject \(H_{0}\) when \(t\leq t_{0}\).

Step2: Check each value

• For \(t = 1.556\): Since \(1.556>1.528\), we reject \(H_{0}\).
• For \(t = 0\): Since \(0<1.528\), we fail to reject \(H_{0}\).
• For \(t = 1.492\): Since \(1.492<1.528\), we fail to reject \(H_{0}\).
• For \(t=-1.567\): The critical region is for \(t>1.528\) (right - tailed test). A negative \(t\) - value is not in the critical region. So we fail to reject \(H_{0}\) because \(t=-1.567<1.528\).

Answer:

(a) Reject \(H_{0}\), because \(t = 1.556>1.528\).
(b) Fail to reject \(H_{0}\), because \(t = 0<1.528\).
(c) Fail to reject \(H_{0}\), because \(t = 1.492<1.528\).
(d) B. Fail to reject \(H_{0}\), because \(t<1.528\).