Question 4: A statistician is trying to find whether there is a relationship between the number of hours of study and exam results, or whether exam results are random. Looking at two different...

Question 4:


A statistician is trying to find whether there is a relationship between the number of hours of study and exam results, or whether exam results are random. Looking at two different subjects, the first part of his study was to generate random numbers of study hours and exam grades, which will be compared to the actual results once the exams are taken and marked. The data randomly generated is given in the table below:

Student	Subject 1 Study Hours	Subject 1 Exam Grade	Subject 2 Study Hours	Subject 2 Exam Grade
1	25	80.0	45	96.0
2	5	8.0	3	29.0
3	18	16.0	14	46.0
4	29	87.0	49	32.5
5	17	95.0	11	61.0
6	39	14.0	19	61.0
7	49	9.5	43	12.0
8	25	10.0	44	46.5
9	6	35.0	0	95.0
10	22	58.0	38	66.0
11	37	8.0	38	24.0
12	31	89.0	50	62.0
13	18	57.0	17	60.5
14	45	22.0	33	10.0
15	5	39.5	33	61.0
16	4	90.0	42	36.0
17	17	23.0	45	39.0
18	29	55.0	34	86.0
19	16	74.0	15	87.0
20	22	29.0	29	100.0
21	28	69.5	49	76.0
22	6	27.0	39	50.5
23	21	12.0	31	55.0
24	4	82.0	14	67.5
25	24	26.0	10	94.0
26	12	13.0	17	33.0
27	4	23.0	34	85.0
28	38	24.5	45	33.0
29	31	77.0	3	19.0
30	5	71.0	44	38.0

Required:

1. Summarise the distribution of expected grades for both exams, according to the data given. Discuss the key characteristics of the data.


2. Construct a 95% confidence interval for the expected exam marks for each of the subjects. Is there a significant difference between them?


3. Would you expect the actual exam results to show a pattern similar to the calculations above? Discuss why/why not and whether you believe the type of exam and questions (numerical, essay-type, multiple choice, etc.) will have an influence in the outcomes.