5. Determine whether to reject or fail to reject the null hypothesis in the following situations: a. $\underline{\underline{t}}[50)=2.35, \alpha=0.01$, one-tailed test to the right b. $\bar{X}_{1}=54, \bar{X}_{2}=44, n_{1}=14, n_{2}=10, s_{\bar{X}_{1}-\bar{X}_{2}}$ O9.85, $\alpha=0.05$, twotailed test c. $95 \%$ Confidence Interval: $(-0.50,2.10)$

Step 1 ：Given the t-value is 2.35, degrees of freedom is 50, and significance level is 0.01 for a one-tailed test to the right.

Step 2 ：Find the critical t-value for a one-tailed test with 50 degrees of freedom and a significance level of 0.01.

Step 3 ：The critical t-value is approximately 2.40.

Step 4 ：Compare the given t-value with the critical t-value. If the given t-value is greater than the critical t-value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Step 5 ：Since the given t-value (2.35) is less than the critical t-value (approximately 2.40), we fail to reject the null hypothesis.

Step 6 ：\(\boxed{\text{Fail to Reject the Null Hypothesis}}\)