Let's break this down step by step:

Part 1:

1. Which test is correct to use, if we do not know the population standard deviation?

   Since we do not know the population standard deviation and we are comparing the means of two independent groups (students who attend classes vs. live-streamers), the appropriate test to use is the t-test (more specifically, an independent samples t-test).

   Answer 1: t-test

2. What is the null hypothesis?

   The null hypothesis for this test would state that there is no difference in the average number of polling quizzes answered by students attending classes and those watching the live stream.

   Answer 2: There is no difference

3. The p-value of the test is 0.938. What is the decision of the test?

   A p-value of 0.938 is much greater than the typical significance level of 0.05. Therefore, we fail to reject the null hypothesis since the result is not statistically significant.

   Answer 3: Do not reject H0

Part 2:

1. Which test is correct to use, if we know the population standard deviation?

   If the population standard deviation is known, then the appropriate test to use is the z-test, which is typically used when the population parameters are known.

   Answer 4: z-test

2. The test statistic is -2.33. This means that the difference between the sample mean and the possible population mean, as stated in the null hypothesis (i.e. 38), is:

   A test statistic of -2.33 indicates that the sample mean is -2.33 times the standard error of the sample mean away from the hypothesized population mean of 38.

   Answer 5: -2.33 times the standard error of the sample mean

3. The p-value of the test is 0.021. What is the decision of the test?

   Since the p-value of 0.021 is less than 0.05, we reject the null hypothesis, concluding that the average number of polling quizzes answered is significantly different from 38.

   Answer 6: Reject H0

Would you like further details or clarification on any of these points?

5 Relative Questions:

1. How would the test change if the sample sizes were very small?
2. What assumptions must be checked before conducting a t-test?
3. How do you interpret the effect size in the context of these tests?
4. What would be the conclusion if the p-value was 0.07 instead of 0.938 in Part 1?
5. How does the confidence interval for the population mean relate to the decision made in Part 2?

Tip: Always verify assumptions like normality and independence before conducting hypothesis tests to ensure the validity of your results.