Final answer:
A directional hypothesis in a paired t-test indicates the expected direction of the difference between the pair means, leading to either a left-tailed or right-tailed test, and not related to alpha, beta, nor directly prescribing the rejection or acceptance of the null hypothesis based on the p-value.
Step-by-step explanation:
A directional hypothesis in a paired t-test stipulates B) The prediction of which of the two means will be larger. This is because a directional hypothesis is concerned with specifying the direction of the expected difference between the two sets of paired data. When formulating the alternative hypothesis (Ha), it defines whether the test will be left-tailed, right-tailed, or two-tailed. This is crucial for conducting the appropriate test.
The null hypothesis (H0) is usually stated with an equal sign, suggesting that there is no effect or difference, while Ha must not contain an equal sign and instead reflects the predicted direction of the difference. For instance, if Ha suggests that the mean difference is greater than zero, this leads to a right-tailed test. Conversely, if Ha indicates the mean difference is less than zero, a left-tailed test is appropriate.
The decision to reject or not reject the null hypothesis is based on comparing the p-value to a predefined level of significance (alpha, α). A smaller p-value indicates stronger evidence against the null hypothesis, whereas a larger p-value suggests weaker evidence. A p-value smaller than alpha usually leads to the rejection of the null hypothesis.