A random sample of 113 students enrolled in statistics units in recent semesters at Macquarie University has been selected to study use of practice quizzes and academic performance. Some of the variables recorded for each student are listed below.

**VariableDescription**

subid

Subject ID

intDom

domestic or international

numQuizzes

the number of practice quizzes attempted

unitMark

the final unit mark

ageGroupCat

the age of students


**Part 1**

**Research question:** we are interested in studying the association between the age of students and their enrolment type (domestic or international) in the population under consideration.
Please complete the following tables, calculating the values of A and B.

Observed count
              | 1 (less than 19) | 2 (19-21) | 3 (22-24) | 4 (more than 24) | Sum
domestic      | A=***            | 11        | 9         | 16               | 56 
international | 11               | 10        | 19        | 17               | 57 
Sum           | 31               | 21        | 28        | 33               | 113

Expected count
              | 1 (less than 19) | 2 (19-21) | 3 (22-24) | 4 (more than 24)
domestic      | 15.363           | 10.407    | 13.876    | B=***           
international | 15.637           | 10.593    | 14.124    | 16.646          

chi-squared
              | 1 (less than 19) | 2 (19-21) | 3 (22-24) | 4 (more than 24)
domestic      | 1.4              | 0.034     | 1.713     | 0.008           
`international | 1.375            | 0.033     | 1.683     | 0.008`           

A [integer]:

Answer 1 Question 2

B [use at least 3dp]

To find values \( A \) and \( B \) for the table, let’s approach each one in steps.

### 1. Finding \( A \) (the missing observed count for domestic students in age group 1)

The total count of domestic students is given as 56. The observed counts for other age groups in the domestic row are already provided:

\[
A + 11 + 9 + 16 = 56
\]

Solving for \( A \):

\[
A = 56 - (11 + 9 + 16) = 56 - 36 = 20
\]

So, \( A = 20 \).

### 2. Finding \( B \) (the missing expected count for domestic students in age group 4)

To calculate \( B \) (the expected count), we use the formula for expected counts in a contingency table:

\[
\text{Expected count} = \frac{\text{Row Total} \times \text{Column Total}}{\text{Grand Total}}
\]

For the domestic row and age group 4, we substitute the values:

\[
B = \frac{56 \times 33}{113} \approx 16.354
\]

Thus, \( B = 16.354 \) (to three decimal places).

### Summary

- \( A = 20 \)
- \( B = 16.354 \)

If you need further clarification on the calculations or want to proceed with additional analysis, please let me know.

---

**Further Related Questions:**

1. What is the interpretation of the chi-squared values in this context?
2. How can we test the statistical significance of the association between age and enrollment type?
3. What are the implications of high or low expected counts on chi-squared analysis accuracy?
4. How does the chi-squared test determine independence between age and enrollment type?
5. Could additional variables affect the relationship between age and enrollment type, and how would we include these in our analysis?

**Tip:** In chi-squared tests, ensure expected counts are sufficiently high (preferably ≥5) for each cell to validate approximation accuracy.

A random sample of 113 students enrolled in statistics units in recent semesters at Macquarie University has been selected to study the use of practice quizzes and academic performance. Some of the variables recorded for each student are listed below. We are interested in studying the association between the age of students and their enrolment type (domestic or international) in the population under consideration. Please complete the following tables, calculating the values of A and B.

This page explains how to calculate observed and expected counts for a chi-squared test, examining the relationship between age group and enrollment type (domestic or international) in a sample of 113 students. Learn how to compute missing values and interpret chi-squared values using contingency tables.

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