You can submit it on eClass at the link “practical work no. 2” or in paper format in class. For electronic submissions, name your document “Your last name + semester + course and activity name”; the activity here is called Practical Work 2. For example, my paper would be titled “Quintin Winter 2023 PSYC2530 Practical Work 2”
Use 2 decimal places for your calculations. You can do your tests and graphic representations by hand or by computer, but you must show your process and/or explain your reasoning. You mustanswer the following questions. You can find an Excel sheet containing the data on eClass.
Here is a table that represents 2 essays that students have had to complete the same statistical exam in a course.
| Student | Examination- 1st test (%) | Examination-2nd test (%) |
| 1 | 59 | 71 |
| 2 | 64 | 63 |
| 3 | 86 | 87 |
| 4 | 74 | 82 |
| 5 | 83 | 89 |
| 6 | 52 | 40 |
| 7 | 57 | 62 |
| 8 | 38 | 55 |
| 9 | 31 | 70 |
| 10 | 74 | 78 |
| 11 | 70 | 78 |
| 12 | 64 | 59 |
| 13 | 40 | 57 |
| 14 | 55 | 59 |
| 15 | 70 | 65 |
1) The professor believes that, on average, students will do better on the second try than on the first.
a) Choose an appropriate test to determine whether students significantly improved on their second try compared to the first and draw a conclusion.
b) Identify the size/magnitude of this effect.
c) Identify the 95% confidence interval around our measurement and explain what this result tells us about our data.
2) I am modifying the table so that column 1 st test now represents the results of students in Professor Calculus’ statistics class and column 2nd test represents the results of a completely different group of students who are in Professor Moriarty’s class .
a) Take a test to show me if there is a significant difference in the performance of Professor Calculus’ students and those of Professor Moriarty.
b) Was the approach used in 2(a) the same as in Question 1? Why or why not?
3) I keep the changes identified in question 2. Column 1always represents the results of students in Professor Calculus’ statistics class and column 2 represents different students in Professor Moriarty’s class. Professor Tournesol discovers that 3 students in his class have cheated so he eliminates their grades from his group. If I wanted to compare the performance of the Sunflower class and the Moriarty class now , should the statistical approach change? Why or why not? (Note: You do not need to do the calculations. You just have to give me an explanation in words.)
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I’m going to change the table a bit. The data now represent the marks obtainedby students in the statistics course in the mid-term examination and in the final examination in 20 2 2.
| Student | Note in the mid-term review (%) | Final exam score (%) |
| 1 | 59 | 71 |
| 2 | 64 | 63 |
| 3 | 86 | 87 |
| 4 | 74 | 82 |
| 5 | 83 | 89 |
| 6 | 52 | 40 |
| 7 | 57 | 62 |
| 8 | 38 | 55 |
| 9 | 31 | 70 |
| 10 | 74 | 78 |
| 11 | 70 | 78 |
| 12 | 64 | 59 |
| 13 | 40 | 57 |
| 14 | 55 | 59 |
| 15 | 70 | 65 |
4) I am interested to know if there is a link between the mark that students obtained in the end-of-term exam and in the final exam.
(a) Make a graphical representation appropriate to this type of data.
b) What conclusions can we draw just by looking at this graph? Is there any data that seems problematic?
5) (a) How strong is the link between these two variables?
(b) How much of the variance could be explained by the relationship between these variables?
c) Is this relationship statistically significant?
6) In the winter semester 2023, a studente obtained 64 in his exam of mi-session. What grade could be predicted that he will get it at the end of the session?
7) a) If I wanted to test the relationship between performance on the mid-term exam and the final exam using a chi-square test, how would the above data table have to be rearranged?
b) Despite my suggestion in 7 a) to use a chi-square test, it would actually be a bad idea to use the chi-square test with this type of problem. Why is this the case? What problem(s) would this cause? (Think about the rules we discussed forthe use of the chi-square.)
