Question

1. What is the random variable in a hypothesis test of two means? [1 sentence]
2. Explain when you use a t-test instead of a z-test statistic for a hypothesis test of two means. [1 sentence]
3. What are the requirements to perform a hypothesis test of two proportions? [3 requirements]
4. Give an example of paired data set. [1 sentence]

Answer 1

1. Difference between 2 sample means is the random variable

2. one uses t test when sample size is less than or equal to 30 and population variance is unknown instead of using Z test

3. a) Samples should be independent

b) For each population, simple random sampling should be used to draw sample

c) each sample should include at least 10 successes and 10 failures

4. suppose we observe marks of students in Statistics before and after giving a course. So these two marks (before taking the course, after taking the course) can be considered as a paired data set.

Thanks!