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.