Hi there, I was looking for any assistance or help on how I would go about starting this assignment? Having difficulty understanding it. Thank you in advance.
"A stats instructor is interested in investigating time of day his lectures were held on student' test scores. He selected a sample of 15 students from his morning (n=7) and evening (n=8) statistics classes and recorded their midterm and final exam scores (shown below). He was interested in examining whether students performed better in morning vs. evening classes on their final exam scores. He also suspected poorer performance on the final exam compared to the midterm among those attending the morning class.
Morning Class (n=7):
Midterm | Final
80 | 59
80 | 64
75 | 65
92 | 70
78 | 67
79 | 58
69 | 79
Evening Class (n=8):
Midterm | Final
62 | 40
70 | 45
80 | 55
78 | 55
84 | 60
64 | 70
84 | 60
64 | 70
84 | 60
64 | 70
84 | 60
70 | 63
The instructor was also curious about what type of exam students preferred to receive in the course (multiple choice or short-answer). He observed the morning class, 6 students preferred multiple choice exams. Evening class, 2 students preferred multiple choice. Does he have evidence that 50% of the students preferred multiple choice exams in the evening class? Finally, can the instructor conclude that there is a relation between test type preference and time of class? If yes, please measure the strength of the relation."
To start the assignment, you need to perform a statistical analysis to determine if there are any significant differences or relationships between variables. In this case, you want to investigate whether there is a difference in test scores between morning and evening classes, as well as any relationship between test type preference and time of class.
Here are the steps you can follow:
1. Organize the data: Create a table to record the midterm and final exam scores for both morning and evening classes. Include the number of students in each class.
Morning Class (n=7):
Midterm | Final
80 | 59
80 | 64
75 | 65
92 | 70
78 | 67
79 | 58
69 | 79
Evening Class (n=8):
Midterm | Final
62 | 40
70 | 45
80 | 55
78 | 55
84 | 60
64 | 70
84 | 60
64 | 70
Additionally, record the number of students in each class who prefer multiple choice exams:
Morning Class: 6 students prefer multiple choice
Evening Class: 2 students prefer multiple choice
2. Analyze the test scores:
a) Calculate the mean (average) and standard deviation of the final exam scores for the morning and evening classes separately. This will give you an overview of the performance in each class.
b) To assess whether the performance in the final exam differs between morning and evening classes, you can perform a hypothesis test. The null hypothesis would be that there is no difference in exam scores between the two classes, and the alternative hypothesis would be that there is a significant difference. You can use a t-test or a non-parametric test (like the Mann-Whitney U test) in this case, as the sample sizes are small.
3. Analyze the test type preference:
a) Calculate the proportion of students who prefer multiple choice exams in the evening class. In this case, it is 2 out of 8, which is 25%.
b) To determine if there is evidence to conclude that 50% of the students in the evening class prefer multiple choice exams, you can perform a hypothesis test. The null hypothesis would be that the proportion is equal to 0.5 (50%), and the alternative hypothesis would be that it is different. You can use a one-sample proportion test (z-test) to assess the difference.
4. Assess the relationship between test type preference and time of class:
To determine if there is a relationship between test type preference and time of class, you can perform a chi-square test for independence. This test will evaluate whether there is a significant association between the two variables. The strength of the relationship can be measured using the phi coefficient or Cramer's V.
Remember to use a statistical software or calculator to perform the calculations and tests for accurate results. Following these steps should help you get started on your assignment and analyze the data effectively.