Statistical Analysis
Topic: Anxiety in college students
Research question: How does anxiety affect students’ academic performance?
Background information
Many a time, college beckons with a chance for a student to live on his or her own, look for new friends, and explore fascinating ideas. However, these changes can be stressful for college students who are craning for a glimpse down the road because when in college, the students separate from their traditional support system from friends and families. Also, they face challenges such as making new friends. Students want to make friends and have relationships during a school year to have someone to talk to during classes or in between classes. But as we all know, trying to make friends is not an easy task, especially when you are new to a school or when you are just antisocial. So, what is the impact of anxiety on the academic performance of the students? The statistical analysis below will provide an answer to this question.
Introduction
I chose this topic because, currently, anxiety is of the issues that adversely affect college students. The students cannot concentrate on their work anymore, just because of fear. Life in college is often difficult, especially for those students who are very anxious to make their own decisions as they are yearning to have their personal experience in life, their levels of anxiety rise, affecting them in the end. Therefore, in the statistical analysis below, I will be looking to determine the extent to which student’s academic performance is affected by anxiety.
Body
Population and sample
The method of sampling I used was random. In my class, which has a population mean of 68 and a total population of 350, I randomly called 210 of my classmates irrespective of their gender, and age-where only 30 responded to my calls and asked them to tell me their recent tests’ scores in mathematics. I was looking for evidence to conclude that anxiety reduces the performance of students. (I took 0.05 as my significance level)
Two students told me they scored 30%
Three students told me they scored 40%
Four students told me they scored 50%
Eight students told me they scored 60%
13 students told me they scored 70%
Data collection and problems encountered in the process
I encountered a problem of getting enough data due to the limited number of a statistical population. As the government’s’ restrictions against the ongoing COVID-19 pandemic don’t allow close contacts, I could not gather enough population to direct my questions to. Therefore, I was forced to call my college friends and ask them the queries.
A bar graph presenting the collected data
Hypothesis testing (p- value method)
Population mean, µ = 60
Sample mean = ∑xi / n = 210/30 = 70
Sample population, n = 30
Sample standard deviation,
= (210-68) squared/ 350 = root of 57.61= 7.59
Denoting the null and alternative hypothesis
H0: μ ≥68
Ha: μ <68
Obtaining the test statistic
From the formula
Z = 70- 68/ (7.59/ sq. root of 30) = 1.44
Calculating p-value
Since this is a one-tailed hypothesis and that the significance level is 0.05, the p-value is 0.0749 when using the standard normal table.
Drawing a conclusion
0.0749 > 0.05, Implying that the p-value is greater than the significance level. Therefore, we don’t reject the null hypothesis. Thus, this data is not providing enough evidence that anxiety reduces the performance of college students.
Conclusively, this statistical analysis didn’t turn out the way I expected because I thought it would turn out in the end that anxiety affects students’ performance. The next time I am doing this, I will ensure that enough statistical population has been gathered.