Final answer:
In a right-tailed t-test with a sample size of 33 and α=0.05, the decision to reject the null hypothesis depends on whether the test statistic t=2.17 is greater than the critical t-value for df=32. If it is greater, reject the null hypothesis; if not, fail to reject it.
Step-by-step explanation:
Understanding the t-Test Decision Process
When performing a right-tailed t-test with a sample size of 33, a test statistic of t=2.17, and a significance level (α) of 0.05, you must compare the test statistic to the critical t-value for a right-tailed test. Since the sample size is 33, the degrees of freedom (df) would be 32 (n-1). You would refer to a t-distribution table or use statistical software to find the critical t-value for df=32 at α=0.05.
Seeing as this is a right-tailed test, if the calculated t-test statistic is greater than the critical t-value, you reject the null hypothesis. Otherwise, you would fail to reject the null hypothesis. For our example, if the critical t-value is less than 2.17, we would reject the null hypothesis indicating that there is a statistically significant result. However, if the critical t-value is more than 2.17, we would fail to reject the null hypothesis indicating that the results are not statistically significant at the 0.05 level.
Comparing p-value and α: An alternative method is to compare the p-value associated with the t-test statistic to the significance level α. If the p-value is smaller than α, this is another indication to reject the null hypothesis. Unfortunately, with the information provided, the specific p-value for t=2.17 with df=32 is not given, thus precluding this comparison.