Final answer:
The accurate interpretation of tobt = 1.972 and tcrit = 2.000 in a t-test is that we fail to reject the null hypothesis, meaning the group means are not significantly different (option A); this being due to the obtained t-value being less than the critical t-value.
Step-by-step explanation:
Based on the results from a t-test where tobt = 1.972 and tcrit = 2.000, the correct interpretation is that we fail to reject the null hypothesis; our group means are not significantly different from one another. This conclusion is drawn because the obtained t-value is less than the critical t-value.
In the context of hypothesis testing, failing to reject the null hypothesis suggests that the observed differences in sample means could have occurred by random chance and are not necessarily indicative of a true effect or difference in the population.
Several examples further illustrate how to interpret t-test results:
- If the t-test value exceeds the critical value or if the p-value is less than the level of significance (α), we reject the null hypothesis, concluding a significant difference.
- When the obtained t-value is within the critical value range, we fail to reject the null hypothesis, accepting that the sample results may be due to chance.
- Use of tools like the calculator function 2-SampTTest or tcdf can help in determining whether to reject or not reject the null hypothesis based upon p-values calculated.