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."
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
Are you going to consider the mid and final test scores separately or pool them?
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.
I'll let you do the calculations.
To start this assignment, you will need to perform statistical analysis on the given data. Here are the steps you can follow:
1. Understand the variables: In this case, we have two variables: time of day (morning or evening) and test scores. We also have another variable, test type preference (multiple choice or short-answer).
2. Define the research questions: In this case, the instructor wants to investigate whether students performed better in morning vs. evening classes on their final exam scores. Additionally, the instructor wants to determine if there is a relation between test type preference and time of class.
3. Analyze test scores based on time of day: Start by comparing the final exam scores of students in the morning class with the final exam scores of students in the evening class. Calculate descriptive statistics such as mean, median, and standard deviation for each group. You can also create a box plot or a histogram to visually compare the distributions.
4. Perform a hypothesis test: To determine if there is a significant difference in final exam scores between morning and evening classes, you can use a statistical test like the independent samples t-test. This test will help you determine if the observed difference in means is statistically significant or if it could have occurred by chance.
5. Analyze test type preference: Calculate the proportion of students who preferred multiple choice exams in both the morning and evening classes. For the evening class, you can compare the observed proportion (2 students) with the hypothesized proportion (50%). You can then perform a hypothesis test using chi-square test or a binomial test to determine if the observed proportion is significantly different from the hypothesized proportion.
6. Assess the relation between test type preference and time of class: To measure the strength of the relation between test type preference and time of class, you can use a statistical measure like Cramér's V or Phi coefficient. These measures quantify the association between categorical variables.
7. Interpret the results: Based on the statistical analysis, you can draw conclusions about the performance difference between morning and evening classes in terms of final exam scores. You can also determine if there is a significant difference in the proportion of students preferring multiple choice exams between morning and evening classes. Finally, you can assess the strength of the relation between test type preference and time of class.
Remember to consult your professor or reference materials for any specific instructions or preferred statistical techniques for this assignment.