hypothesis testing

Hi Can any one help me with this please as i don't know how to do this question? Please look at the formulas and tell me which formula to use? i know n=100, mean=44.22, variance=482, sample variance=487 so which formula to use? and how do i do the test? thank you

Marks ≥ 40%result in a pass, while marks < 40% result in a fail. Test the hypothesis that passing/failing this module is independent of the number of attendances,in the following steps:

1. Determine what test you should perform (name!) and justify
2. Determine what quantity to look at,and which distribution table to use, justifying your choice.
3. Determine the number of degrees of freedom, justifying you answer.
4. Determine the P-value of this test(interpolate if necessary).
5. Interpret your findings, and provide a conclusion in words.

It would be helpful if you could post the whole question. In particular, we need to know something about the form in which you are given "attendances".

Each line represents a student enrolled on the module AM10MT (MathematicalThinking) in the academic year 2015-16.The number in the left column (X-value) is the number of registered lectureattendances (a number between 0 and 11) and the right column (Y -value) isthe final overall mark of that student for this module (a percentage between0 and 100%).

Lectures | Marks 11 90 11 79 11 79 11 75 11 72 11 72 11 71 11 71 11 70 11 70 11 69 11 68 11 64 11 60 11 54 11 52 11 52 11 51 11 46 11 38 11 32 11 31 11 31 10 89 10 82 10 80 10 75 10 71 10 61 10 60 10 57 10 43 10 39 10 37 10 33 10 23 9 71 9 62 9 56 9 49 9 49 9 48 9 20 8 68 8 62 8 57 8 56 8 54 8 51 8 49 8 48 8 45 8 44 8 39 8 37 8 25 7 67 7 52 7 38 7 34 7 26 7 11 7 10 7 2 6 63 6 45 6 45 6 42 6 35 6 9 5 59 5 50 5 50 5 29 5 13 4 42 4 32 4 13 4 7 3 49 3 31 3 25 3 25 2 48 2 30 2 30 2 11 1 36 1 32 1 29 1 1 0 49 0 36 0 32 0 25 0 22 0 0 0 0 0 0 0 0

The way I would analyse this is to use binary logistic regression with pass/fail as the outcome variable and with the number of sessions attended as the explanatory variable.

However, I suspect that you're looking for something more elementary. A reasonable approach would be to test for a difference of mean number of attendances in the group that pass versus the group that fails. If you have to estimate the population mark standard deviation, then this will be a t-test (i.e. your case 1). If you know the population standard deviation, then you can use a z-test (your case 2). In your OP you state that you know that variance = 482, but I don't see where you've got that from in the question.

One little wrinkle to look out for: at the bottom of your dataset you have a number of "0 0" entries. You're going to have to think about what these entries mean and whether they should be included in the analysis.