Question 8 of 21 This test: 21 point(s) possible This question: 1 point(s) possible Submit test State whether the standardized test statistic $t$ indicates that you should reject the null hypothesis. Explain. (a) $\mathrm{t}=-2.196$ (b) $\mathrm{t}=2.041$ (c) $\mathrm{t}=2.131$ (d) $\mathrm{t}=-2.171$ (a) For $t=-2.196$, should you reject or fail to reject the null hypothesis? A. Reject $\mathrm{H}_{0}$, because $\mathrm{t}>2.108$. B. Fail to reject $\mathrm{H}_{0}$, because $\mathrm{t}<-2.108$. C. Reject $\mathrm{H}_{0}$, because $\mathrm{t}<-2.108$. D. Fail to reject $\mathrm{H}_{0}$, because $-2.108<\mathrm{t}<2.108$ Next
Solution
Step 1 ：The question is asking whether we should reject or fail to reject the null hypothesis based on the value of the t-statistic. The decision to reject or fail to reject the null hypothesis is based on the comparison of the absolute value of the t-statistic with the critical value.
Step 2 ：If the absolute value of the t-statistic is greater than the critical value, we reject the null hypothesis. If it is less than or equal to the critical value, we fail to reject the null hypothesis. In this case, the critical value is 2.108.
Step 3 ：For t = -2.196, the absolute value is 2.196 which is greater than the critical value 2.108. Therefore, we should reject the null hypothesis.
Step 4 ：Final Answer: \(\boxed{\text{C. Reject } H_{0}, \text{ because } t<-2.108}\)
