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A random sample of 136 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 the average number of practice quizzes attempted equal to 38?’
Which test is correct to use, if we do not know the population standard deviation?	Answer 1 Question 1
 
The test statistic is -1.1. This means that the difference between the sample mean and the possible population mean, as stated in the null hypothesis (i.e. 38), is:	Answer 2 Question 1
 
The p-value of the test is 0.274. What is the decision of the test?	Answer 3 Question 1
 
Part 2
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 know the population standard deviation?	Answer 4 Question 1
 
What is the null hypothesis?	Answer 5 Question 1
 
The p-value of the test is 0.612. What is the decision of the test?	Answer 6 Question 1
 
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### Part 1

**Answer 1 (Test to Use When Population Standard Deviation is Unknown):**  
When the population standard deviation is unknown, and we are testing whether the average number of practice quizzes attempted equals 38, the appropriate test is a *one-sample t-test*. This is because we are dealing with a single sample, and the population standard deviation is not provided.

**Answer 2 (Interpretation of the Test Statistic -1.1):**  
The test statistic of -1.1 means that the sample mean is 1.1 standard errors below the hypothesized population mean of 38 quizzes. In other words, the sample mean is close to 38 but slightly lower.

**Answer 3 (Decision Based on a p-value of 0.274):**  
The p-value of 0.274 is higher than the conventional significance level of 0.05. Therefore, we **fail to reject the null hypothesis**. This means there is not enough evidence to conclude that the average number of practice quizzes attempted differs from 38.

### Part 2

**Answer 4 (Test to Use When Population Standard Deviation is Known):**  
If the population standard deviation is known, and we are comparing the average number of practice quizzes between domestic and international students, the appropriate test would be a *two-sample z-test*. This is because we are comparing two independent groups and have the population standard deviation.

**Answer 5 (Null Hypothesis for Comparing Domestic and International Students):**  
The null hypothesis for this test would be:  
**H₀**: There is no difference between domestic and international students in the average number of practice quizzes attempted.  
Mathematically, this can be expressed as:  
**H₀**: μ_domestic = μ_international

**Answer 6 (Decision Based on a p-value of 0.612):**  
The p-value of 0.612 is much greater than the typical significance level of 0.05. Therefore, we **fail to reject the null hypothesis**. This means there is no statistically significant difference between the average number of practice quizzes attempted by domestic and international students.

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Would you like more details on any part of this question?

Here are some related questions you might find useful:
1. What assumptions must be verified before conducting a t-test?
2. How do you calculate a p-value manually from a test statistic?
3. What are Type I and Type II errors in hypothesis testing?
4. How do z-tests and t-tests differ in terms of application?
5. What does statistical significance mean in practical terms?

**Tip:** When the p-value is larger than 0.05, it indicates weak evidence against the null hypothesis, meaning the data does not provide sufficient grounds to reject it.

A random sample of 136 students enrolled in statistics units in recent semesters at Macquarie University has been selected to study use of practice quizzes and academic performance. 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 the average number of practice quizzes attempted equal to 38?' Which test is correct to use, if we do not know the population standard deviation? The test statistic is -1.1. The p-value of the test is 0.274. What is the decision of the test? Part 2: 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 know the population standard deviation? What is the null hypothesis? The p-value of the test is 0.612. What is the decision of the test?

Explore hypothesis testing methods with a real-world problem. Learn how to perform a one-sample t-test when the population standard deviation is unknown and a two-sample z-test for comparing quiz attempts between domestic and international students. Understand test statistics, p-value interpretation, and decision-making. Suitable for undergraduate statistics students.

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