# Population & Sample Size Questions

1.Why would you use a small sample to draw inference about a large population?

Test of a single proportion:

2. What is the difference between a sample parameter (X-bar and s) and a proportion parameter (p)?

Test of two populations, large sample size (z-statistics)

3. When would you use two population test with a large sample size in your education?

Test of two populations, small sample size (t-statistics)

4. When would you use two population test with a small sample size in your education?

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#### Solution Preview

Please see the attached file.

Test of single population, small sample size (t-statistics)

1. Why would you use a small sample to draw inference about a large population?

When the assumption required for a large-sample test of hypothesis about m is violated, we need a hypothesis-testing procedure that is appropriate for use with small samples, because if we use methods of the large-sample test there will be following errors:

(i) the small sample will ...

#### Solution Summary

Solution attaches a Word file which explains why and how to use sample sizes as accurate representations of populations, and the concept of z- and t-test statistics within this.