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 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. (c) for t = 1.977, should you reject or fail to reject the null hypothesis? a. fail to reject h₀, because t < 2.033. b. fail to reject h₀, because t > 2.033. c. reject h₀, because t > 2.033. d. reject h₀, because t < 2.033.

Explanation:

Step1: Analyze the rejection rule

In a one - tailed t - test (right - tailed in this case as the critical region is on the right side with \(t_{\alpha}=2.033\)), we reject the null hypothesis \(H_0\) if the test statistic \(t\) is in the rejection region (i.e., \(t>t_{\alpha}\)) and fail to reject \(H_0\) if \(t\leq t_{\alpha}\).

Step2: Compare \(t = 1.977\) with \(t_{\alpha}=2.033\)

We have \(t = 1.977\) and \(t_{\alpha}=2.033\). Since \(1.977<2.033\) (i.e., \(t

Answer:

A. Fail to reject \(H_0\), because \(t < 2.033\)