Final answer:
A t value of 3.32 means the observed difference is 3.32 times the expected difference under the null hypothesis and indicates a statistically significant difference, leading to rejection of the null hypothesis. The corresponding p-value is approximately 0.0103, which reinforces this decision.
Step-by-step explanation:
If your obtained t value is 3.32, this indicates that the observed difference between the means is 3.32 times greater than what would be expected if the null hypothesis were true (that is, no difference or effect). In statistical terms, the t value is a measure of how many standard errors the observed effect is away from the null hypothesis expectation.
When comparing to a critical value, which for a two-tailed test at an alpha level of 0.05 with 24 degrees of freedom is 2.064, a t value of 3.32 is higher. This suggests that you would reject the null hypothesis, as your obtained t value falls in the critical region where the observed data is unlikely under the null hypothesis. Therefore, you can conclude that there is a statistically significant difference or correlation between the variables studied.
To further quantify this, you could calculate the p-value, which is the probability of getting a t value as extreme as, or more extreme than, what was observed, if the null hypothesis were true. A p-value less than the chosen alpha level suggests rejection of the null hypothesis, hence supporting the presence of a statistically significant effect. And according to the given information, the p-value for a t value of 3.32 would be approximately 0.0103, which is indeed less than standard alpha level 0.05, intensifying the evidence against the null hypothesis.