A random sample of 126 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.

Variable	Description
subid	Subject ID
intDom	domestic or international
numQuizzes	the number of practice quizzes attempted
unitMark	the final unit mark
Address the following questions, assuming as necessary that all test assumptions are verified.
Part 1
A test is run to answer the research question, ’Is there any difference between domestic students and international students in the average number of practice quizzes attempted?’ Which test is correct to use, if we do not know the population standard deviation?

To answer the research question, "Is there any difference between domestic students and international students in the average number of practice quizzes attempted?", the correct statistical test to use is a **two-sample independent t-test**. This is because:

1. **Two groups involved**: You are comparing two independent groups (domestic students vs. international students).
2. **Continuous variable**: The number of practice quizzes attempted is a continuous numerical variable.
3. **Unknown population standard deviation**: Since the population standard deviation is not known, the t-test is more appropriate than a z-test.
4. **Testing for differences in means**: The goal is to compare the average number of quizzes attempted between the two groups.

**Key Assumptions**:
- The number of quizzes attempted is normally distributed in each group, or the sample sizes are sufficiently large for the Central Limit Theorem to apply.
- The variances of the two groups are approximately equal (if not, you could use a version of the t-test that does not assume equal variances, such as Welch's t-test).

Would you like more details on how to perform this test, or how to interpret the results?

Here are five related questions to expand your understanding:

1. How do we check if the variances of the two groups are equal?
2. What is Welch's t-test, and when should it be used instead of the regular t-test?
3. How do we interpret the p-value obtained from the two-sample t-test?
4. What role does the Central Limit Theorem play in justifying the use of the t-test?
5. How could non-normality of data affect the results of the t-test?

**Tip**: Always check assumptions before performing a statistical test, as violations may lead to inaccurate conclusions.

A test is run to answer the research question, 'Is there any difference between domestic students and international students in the average number of practice quizzes attempted?' Which test is correct to use, if we do not know the population standard deviation?

Explore the use of a two-sample t-test to determine if there is a significant difference in the average number of practice quizzes attempted by domestic and international students. This page covers key statistical concepts, including hypothesis testing, the Central Limit Theorem, and Welch's t-test. Suitable for undergraduate students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation