Question 8
The BA discourse is often cluttered with queries / requests related to solutions for Past Year Question Papers (PYQP). The course instructor, Dr. Milo, had been informing that students need to put in effort to find solutions by searching the discourse. However, the results seem to disappointing. Therefore, Dr. Milo wanted to do a few basic analytics on discourse behaviour of students. Past student data was collected for the analysis.
Past data was collected for the BA terms in Jan-2022, May-2022, Sep-2022, Jan-2023, May-2023 and Sep-2023. For each term, 100 randomly selected unique student IDs were sampled. Of the 100 student IDs, 50 were “Male” and the remaining were “Female”. The learners in the discourse have either “followed the instructions” or “not followed the instructions” or “have not accessed the discourse at all” (these three are referred to as access categories). Specifically, for the sample data in the different terms (in sequence of earliest term to latest term i.e. Jan-2022 to Sep-2023) it was observed that
• For the Male sample: 20, 30, 25, 45, 25 and 35 had followed the instructions (respectively in each term i.e 20 male learners had followed the instructions in Jan-2022 term and so on)
• For the Male sample: 2, 10, 5, 4, 5 and 3 had not accessed discourse at all (respectively in each term i.e 2 male learners had not accessed discourse at all in Jan-2022 term and so on) • For the female sample: 15, 22, 32, 25, 20 and 20 had followed the instructions (respectively in each term i.e 15 female learners had followed the instructions in Jan-2022 term and so on) and the remaining learners in the respective female sample had not followed the instructions Moreover, Dr. Milo assumes that all learners in the “followed the instructions” category are Normally distributed with a mean of 18 and standard deviation of 4. Each BA term is taken as a sample point to identify the required counts (for this specific analysis). A binning of data is performed with the following three bins (which capture the number of learners who follow the instructions in a sample). The bins divide the solution space into equal areas.
Bin-1: [less than or equal to 35]
Bin-2: [36 to less than or equal to 50]
Bin-3: [51 to less than or equal to 100]
Given this information, answer the subquestions
How many degrees of freedom is present for the hypothesis test used to check if Dr. Milo’s assumption that all learners in the “followed the instructions” category are Normally distributed?