Final answer:
The statement in question represents a 'Two-tailed null hypothesis' because it assumes there is no difference in performance between students in an online course and those in a face-to-face class, which is tested against an alternative hypothesis in hypothesis testing.
Step-by-step explanation:
The statement 'Students in an online course perform the same as students in a face-to-face class' is representative of a hypothesis comparing two means, specifically it's the null hypothesis. To test such a hypothesis, the professor must determine if there is a statistically significant difference between the two modes of learning. In hypothesis testing, a two-tailed null hypothesis assumes that there is no difference between the groups. Option C 'Two-tailed null hypothesis' is the correct answer because the statement suggests that there is no difference in performance between the two groups. The alternative hypothesis would specify a direction (if students perform better or worse in one condition), and since the provided statement does not suggest a direction, it is a two-tailed test.
For example, if a professor wanted to compare final exam scores between an online class and a face-to-face class, the null hypothesis (H0) would be that the means of the final exam scores are equal. The alternative hypothesis (Ha) might suggest that the mean of the online class is not equal to the mean of the face-to-face class, which in a testing scenario would be a two-tailed test if the professor is checking for any difference in both directions (online scores being higher or lower). If the p-value from the test statistics is smaller than the significance level (< 0.05), this would lead to rejection of the null hypothesis because it would indicate a significant difference in means.