All of the above must be known in order to determine whether a t test is statistically significant. Hence the correct option is d.
To determine whether a t-test is statistically significant, several key factors must be considered. The degrees of freedom (option a) are crucial for determining the appropriate t-distribution and are calculated based on the sample size (option b). The sample size itself is significant as it influences the precision and reliability of the results; larger samples often provide more reliable estimates.
Additionally, understanding whether it is a one-tailed or two-tailed test (option c) is essential, as it dictates how extreme the observed results must be to be considered statistically significant. Therefore, all of the mentioned factors—degrees of freedom, sample size, and the type of t-test—play integral roles in determining the statistical significance of a t-test, making option d, "all of the above," the correct choice. Furthermore, each of these factors can individually or collectively have a significant effect (option e) on the outcome of the t-test. Hence the correct option is d.