Statistical Analysis of Gender and Year in College - Assignment

This assignment investigates the relationship between gender and the year in college using a chi-square test for independence. The student analyzes a dataset to determine if these two variables are statistically independent. A contingency table is created to illustrate the data distribution, and the null hypothesis, stating no relationship, is tested against the alternative hypothesis. The chi-square test results, including the test statistic, p-value, and critical value, lead to the conclusion that gender and year in college are independent. This implies that a student's gender does not predict their year of study, and vice-versa. The analysis includes references to statistical methods and relevant literature.

Running head: GENDER AND THE YEAR IN COLLEGE
Is Gender and the Year in College Independent?
Name:
Institution:

GENDER AND THE YEAR IN COLLEGE
Chi-square test for independence is applied when the data are in a contingency table to
determine whether two groups of a population of nominal data are statistically independent
(Keller, 2014). This, chi-square test for the contingency table (test for independence) helps in
making inference on whether two groups of the population data are related. This task will
assess whether the sex and the year in college are independent. The cross-classification tables
are important in illustrating the data distribution. This was carried out and the results are as
illustrated below.
Sex
year in college F M Total
Freshman 5 5 10
Juniors 5 5 10
Seniors 5 5 10
sophomores 5 5 10
Total 20 20 40
The chi-square test hypothesis is:
H0: the sex and the year in college are not related
Ha: sex and the year in college are related
The test results are as follows.
Data
Level of Significance 0.05
Number of Rows 4
Number of Columns 2
Degrees of Freedom 3
Results
Critical Value 7.814727903
Chi-Square Test Statistic 0
p-Value 1
Do not reject the null hypothesis
The results suggest that there is insufficient to reject the null hypothesis ( χ(3)
2 = 0.00, p-value
> 0.05) (Sharpe, 2015). Thus, we conclude that sex and the year in college are related. In
other words, we can infer that the gender of the student and the year in college are

GENDER AND THE YEAR IN COLLEGE
independent of one another. This implies that a student is randomly selected from the
population, he/she is equally likely to come from any gender or any year. The results also
mean that if the college/institution wants to predict the number of students in the different
study year, they can’t use gender since these two are not related. Further, it means that
whether a student is a male or female, it does not affect their year of study.

GENDER AND THE YEAR IN COLLEGE
References
Keller, G. (2014). Statistics for Management and Economics (10th ed.). Stamford: Cengage
Learning.
Sharpe, D. (2015). Your chi-square test is statistically significant: now what? Practical
Assessment, Research & Evaluation, 20(8), 1-10.