https://file.aiquickdraw.com/mathbot/file/1726121303873isaarx8l.jpg

Let's break down the statistical analysis from the image and provide answers:

### Part 1
The research question is asking if there's any difference between domestic and international students in the average number of practice quizzes attempted.

1. **Which test is correct to use, if we do not know the population standard deviation?**
   - The appropriate test to use here is a **t-test**, specifically an independent samples t-test since it compares two different groups (domestic vs. international students), and the population standard deviation is unknown.

2. **What is the null hypothesis?**
   - The null hypothesis (\(H_0\)) is: **There is no difference in the average number of practice quizzes attempted between domestic and international students.**

3. **The p-value of the test is 0.244. What is the decision of the test?**
   - Since the p-value (0.244) is greater than the common significance level (typically 0.05), the decision is to **not reject the null hypothesis**. This means there is not enough evidence to suggest a difference in the average number of practice quizzes attempted between domestic and international students.

### Part 2
The second research question asks if the average number of practice quizzes attempted is equal to 38.

1. **Which test is correct to use, if we know the population standard deviation?**
   - Since the population standard deviation is known, the correct test to use here is a **z-test**.

2. **The test statistic is -1.5. This means that the difference between the sample mean and the possible population mean (38) is...**
   - The difference is negative, implying that the sample mean is **less than** the hypothesized population mean of 38 quizzes.

3. **The p-value of the test is 0.136. What is the decision of the test?**
   - The p-value of 0.136 is greater than 0.05, so the decision is to **not reject the null hypothesis**. This means there is insufficient evidence to conclude that the average number of practice quizzes attempted is different from 38.

### Do you need further clarification on any part of this analysis?

Here are five related questions to deepen understanding:
1. What is the difference between a t-test and a z-test?
2. How do you interpret p-values in hypothesis testing?
3. What are Type I and Type II errors in hypothesis testing?
4. How does the sample size affect the t-test and z-test?
5. What assumptions need to be met for using a t-test?

**Tip:** Always check whether the assumptions for the t-test or z-test are met, including normality of the data and independent samples.

A random sample of 115 students enrolled in statistics units in recent semesters at Macquarie University was taken to study the use of practice quizzes and academic performance. The following research questions are asked: 1. Is there any difference between domestic and international students in the average number of practice quizzes attempted? 2. Is the average number of practice quizzes attempted equal to 38?

This problem explores hypothesis testing using t-tests and z-tests to determine whether there is a significant difference between domestic and international students' quiz attempts. It also tests if the average number of quizzes attempted is equal to 38. The study is based on a random sample of 115 students at Macquarie University.

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