Question
In: Statistics and Probability
On Moodle, you will find a file labelled “Data for Question 4 Assignment 1”. It contains...
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On Moodle, you will find a file labelled “Data for Question 4 Assignment 1”. It contains data on past students in this course. Under Midterm is information on whether past studentsgot an A grade (A−, A, A+) an F or D grade (D is a passing grade but most students need aC− for it to count towards their program) or Other (any grade in between). Under FinalExam is information on whether students got a D or F grade or anything “better”.
Conduct a test of independence to determine if the Midterm grades are independent of final exam grades. So we can better compare our answers, make Final Exam your row variable and Midterm your column variable. Use α = 0.01.
I attached the table provided below! Please show me or take picture of the excel procedure. This assignment is due in 5 hours if someone could answer before this time I will be ETERNALLY grateful and rate the highest possible, thanks.
| Observation | Midterm | Final Exam |
| 1 | F or D | F or D |
| 2 | F or D | F or D |
| 3 | Other | F or D |
| 4 | F or D | Better |
| 5 | F or D | F or D |
| 6 | F or D | F or D |
| 7 | A grades | Better |
| 8 | Other | F or D |
| 9 | A grades | Better |
| 10 | A grades | Better |
| 11 | F or D | F or D |
| 12 | A grades | Better |
| 13 | F or D | F or D |
| 14 | A grades | Better |
| 15 | F or D | Better |
| 16 | F or D | F or D |
| 17 | F or D | F or D |
| 18 | Other | Better |
| 19 | F or D | F or D |
| 20 | F or D | Better |
| 21 | Other | F or D |
| 22 | F or D | F or D |
| 23 | A grades | Better |
| 24 | A grades | Better |
| 25 | A grades | Better |
| 26 | F or D | F or D |
| 27 | F or D | F or D |
| 28 | Other | F or D |
| 29 | F or D | F or D |
| 30 | Other | F or D |
| 31 | F or D | F or D |
| 32 | Other | Better |
| 33 | F or D | Better |
| 34 | F or D | Better |
| 35 | F or D | F or D |
| 36 | F or D | F or D |
| 37 | F or D | F or D |
| 38 | F or D | F or D |
| 39 | F or D | F or D |
| 40 | F or D | F or D |
| 41 | Other | F or D |
| 42 | Other | F or D |
| 43 | F or D | F or D |
| 44 | Other | F or D |
| 45 | A grades | Better |
| 46 | Other | F or D |
| 47 | F or D | F or D |
| 48 | A grades | F or D |
| 49 | F or D | F or D |
| 50 | A grades | Better |
| 51 | F or D | F or D |
| 52 | F or D | F or D |
| 53 | F or D | F or D |
| 54 | Other | F or D |
| 55 | F or D | F or D |
| 56 | A grades | Better |
| 57 | A grades | Better |
| 58 | Other | F or D |
| 59 | A grades | Better |
| 60 | Other | F or D |
| 61 | A grades | F or D |
| 62 | F or D | F or D |
| 63 | Other | F or D |
| 64 | Other | F or D |
| 65 | F or D | F or D |
| 66 | A grades | F or D |
| 67 | A grades | F or D |
| 68 | Other | F or D |
| 69 | Other | F or D |
| 70 | F or D | F or D |
| 71 | Other | F or D |
| 72 | Other | F or D |
| 73 | A grades | Better |
| 74 | A grades | F or D |
| 75 | Other | F or D |
| 76 | F or D | F or D |
| 77 | F or D | F or D |
| 78 | F or D | F or D |
| 79 | F or D | F or D |
| 80 | Other | F or D |
| 81 | F or D | F or D |
| 82 | F or D | F or D |
| 83 | A grades | Better |
| 84 | F or D | F or D |
| 85 | F or D | F or D |
| 86 | F or D | F or D |
Solutions
Expert Solution
First of all data is sorted and compressed in MS-EXCEL:
- Data in Excel
- Sort Option on right corner
- Select Midterm using levels in "Sort by" dialog box
- Add next level
Final Sorted data that one obtains:
| Observation | Midterm | Final Exam |
| 7 | A grades | Better |
| 9 | A grades | Better |
| 10 | A grades | Better |
| 12 | A grades | Better |
| 14 | A grades | Better |
| 23 | A grades | Better |
| 24 | A grades | Better |
| 25 | A grades | Better |
| 45 | A grades | Better |
| 50 | A grades | Better |
| 56 | A grades | Better |
| 57 | A grades | Better |
| 59 | A grades | Better |
| 73 | A grades | Better |
| 83 | A grades | Better |
| Observation | Midterm | Final Exam |
| 48 | A grades | F or D |
| 61 | A grades | F or D |
| 66 | A grades | F or D |
| 67 | A grades | F or D |
| 74 | A grades | F or D |
| Observation | Midterm | Final Exam |
| 4 | F or D | Better |
| 15 | F or D | Better |
| 20 | F or D | Better |
| 33 | F or D | Better |
| 34 | F or D | Better |
| Observation | Midterm | Final Exam |
| 1 | F or D | F or D |
| 2 | F or D | F or D |
| 5 | F or D | F or D |
| 6 | F or D | F or D |
| 11 | F or D | F or D |
| 13 | F or D | F or D |
| 16 | F or D | F or D |
| 17 | F or D | F or D |
| 19 | F or D | F or D |
| 22 | F or D | F or D |
| 26 | F or D | F or D |
| 27 | F or D | F or D |
| 29 | F or D | F or D |
| 31 | F or D | F or D |
| 35 | F or D | F or D |
| 36 | F or D | F or D |
| 37 | F or D | F or D |
| 38 | F or D | F or D |
| 39 | F or D | F or D |
| 40 | F or D | F or D |
| 43 | F or D | F or D |
| 47 | F or D | F or D |
| 49 | F or D | F or D |
| 51 | F or D | F or D |
| 52 | F or D | F or D |
| 53 | F or D | F or D |
| 55 | F or D | F or D |
| 62 | F or D | F or D |
| 65 | F or D | F or D |
| 70 | F or D | F or D |
| 76 | F or D | F or D |
| 77 | F or D | F or D |
| 78 | F or D | F or D |
| 79 | F or D | F or D |
| 81 | F or D | F or D |
| 82 | F or D | F or D |
| 84 | F or D | F or D |
| 85 | F or D | F or D |
| 86 | F or D | F or D |
| Observation | Midterm | Final Exam |
| 18 | Other | Better |
| 32 | Other | Better |
| Observation | Midterm | Final Exam |
| 3 | Other | F or D |
| 8 | Other | F or D |
| 21 | Other | F or D |
| 28 | Other | F or D |
| 30 | Other | F or D |
| 41 | Other | F or D |
| 42 | Other | F or D |
| 44 | Other | F or D |
| 46 | Other | F or D |
| 54 | Other | F or D |
| 58 | Other | F or D |
| 60 | Other | F or D |
| 63 | Other | F or D |
| 64 | Other | F or D |
| 68 | Other | F or D |
| 69 | Other | F or D |
| 71 | Other | F or D |
| 72 | Other | F or D |
| 75 | Other | F or D |
| 80 | Other | F or D |
See bottom right corner will give respective counts i.e. observed frequency.
Theory and Computation:
| Midterm | Final Exam | Count | Eij | Oij | (Oij-Eij) | (Oij-Eij)^2/Eij | |||
| A grades | Better | 15 | 64*20/86 | 14.88372 | 5 | -9.88372 | 6.563408 | ||
| A grades | F or D | 5 | 22*20/86 | 5.116279 | 15 | 9.883721 | 19.09355 | ||
| F or D | Better | 5 | 64*44/86 | 32.74419 | 39 | 6.255814 | 1.19518 | ||
| F or D | F or D | 39 | 22*44/86 | 11.25581 | 5 | -6.25581 | 3.476888 | ||
| Other | Better | 2 | 64*22/86 | 16.37209 | 20 | 3.627907 | 0.803911 | ||
| Other | F or D | 20 | 22*22/86 | 5.627907 | 2 | -3.62791 | 2.338651 | ||
| 86 | 33.47159 | ||||||||
| Critical value | |||||||||
| df=(m-1)(n-1) | (2-1)*(3-1) | 2 | |||||||
| chitab | CHIINV(0.05,2) | 5.991465 | |||||||
| chical > chitab, we Reject H0. | |||||||||
No, Midterm grades are not independent of final exam grades.
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