Question

After receiving their mid-term grades, four students formed a study group. On writing assignments they have turned in since forming the study group, the students’ responses are “too” similar, almost to the point of being exact copies. Recognizing these similarities might have resulted from the common wording the students use while studying, their teacher cannot decide whether to forget the situation or accuse the students of academic dishonesty. Expressed in words, not symbols, what are the null and alternative hypotheses in this situation? Explain why you chose these as the hypotheses and What you would to test you hypotheses?

Answer 1

In this case, the aim is to test whether the performance of the students after forming the 'study group' should be considered as a case of academic dishonesty or not. so the Null Hypothesis should be the hypothesis of no difference, that is,

Null Hypothesis : Students should not be accused of Academic Dishonesty, that is, there is no significant difference between the performance of students before and after forming the study group.

Alternative Hypothesis : Students should be accused of academic dishonesty, that is, there is significant difference between the performance of students before and after performing the study group

These are the correct hypotheses because if the samples of their marks collected before forming the study group show a significant difference from the samples of their marks collected after forming the study group, then the teacher should suspect them of academic dishonesty. However, if the difference between the two samples is by chance, then the two samples will not show significant difference and the null hypothesis will be accepted.

We can apply paired t-test for analysing the difference between the marks of the students before forming the study group and after forming the study group. Paired t-test can be applied since the two samples come from the populations with same variance.