Question

Suppose that we want to investigate whether curfews correlate with differences in grades for students in middle school. We select a random sample of 81 middle school students. The variables are curfew (yes/no) and grade (a letter grade that represents the average grade across courses). Is there an association between grade and curfew? Or are these two variables independent? We use the data to conduct a chi-square test of independence at the 5% level. In this print-out, the observed count appears above the expected count in each cell. What can we conclude?

Answer 1

Answer:

Step-by-step explanation:

Hello!

Given the variables

X: Curfew of middle school students (Categorized Yes/No)

Y: Average grade of middle school students. (Categorized: A, B, C, and D)

The objective is to test if there is an association between both variables, you have to conduct a Chi-Square test of independence.

In the null hypothesis, you state that both variables are independent vs. the alternative hypothesis that the variables are dependent.

The hypotheses for this test are:

H₀: Pij= Pi. * P.j i= (1)Yes, (2)No; j= (1)A, (2)B, (3)C, (4)D

H₁: Te variables are not independent.

α: 0.05

$X^2= sum\frac{(O_{ij}-E_{ij})^2}{E_{ij}} ~~X_{(r-1)*(c-1)}$

Where

Oij is the observed frequency for the i-row and j-column

Eij is the expected frequency for the i-row and j-column

r= number of categories in the rows

c= number of categories in the columns

$X^2_{H_0}= 1.4796703$

p-value: 0.687

The p-value is greater than the significance level, so the decision is to not reject the null hypothesis. So using a 5% significance level, you can conclude that having a curfew and the average grades of middle schoolers are two independent variables.