# Chapter 5: Sampling Distributions

Answers for all ‘Test Yourself’ questions from the book to check your performance and widen your overall understanding of the contents.

1.
1. When we have a single population we want to draw randomly from to get as accurate a picture of that population as possible.
2. When we want to use simple random sampling, but we’re worried that particular subgroups within our population won’t be adequately represented if we rely solely on simple random sampling.
3. When this is the only type of sampling available to us.
2. The colours don’t matter; chance doesn’t pay attention to colour.  There is an equal probability of drawing any particular marble any time.  For this purpose, let’s label the marbles M1, M2, M3, M4 and M5.  There are 20 possible draws:
1. M1, M2
2. M1, M3
3. M1, M4
4. M1, M5
5. M2, M1
6. M2, M3
7. M2, M4
8. M2, M5
9. M3, M1
10. M3, M2
11. M3, M4
12. M3, M5
13. M4, M1
14. M4, M2
15. M4, M3
16. M4, M5
17. M5, M1
18. M5, M2
19. M5, M3
20. M5, M4
3. 40 women and 10 men, which he would identify with stratified random sampling.
4. There is one sampling distribution for any given population at any particular sample size.  Therefore, the answer is 1.
5. Our best guess as to the population standard error is also 1.  But we can’t know what it is definitively with this information alone.