Final answer:
Your data is not significantly different because the t-test value of 3.45 is less than the critical value of 3.46. To declare a significant difference, the t-test value must exceed the critical value. The p-value can also provide guidance in borderline cases.
Step-by-step explanation:
If your t-test value is t=3.45 and the critical value is CV=3.46, your data is not significantly different. This is because the t-test value needs to be greater than the critical value in order to reject the null hypothesis and conclude that there is a significant difference. In statistical hypothesis testing, the critical value represents a threshold at which you would consider the results statistically significant. Since your t-test value is slightly less than the critical value, you fail to reject the null hypothesis, indicating no evidence of a significant difference.
Additionally, when you compare a p-value to a significance level (commonly denoted as α), if the p-value is less than α, you reject the null hypothesis. For instance, if α = 0.05 and the p-value is 0.026, you would reject the null hypothesis since the p-value is smaller, indicating significant results. In cases where you have a t-test value close to the critical value, referring to the p-value can further guide your decision.