Question

9. Statisticians prefer large samples. Describe briefly the effect of increasing the size of a sample (or the number of subjects in an experiment) on each of the following:

PLEASE EXPLAIN WHY

a. 95% confidence interval

b. The ??-value of a test, when ??0 is false and all facts about the population remain unchanged as ?? increases.

Answer 1

(a)

The effect of increasing the size of the sample on 95% confidence interval:

Decreases the width of the confidence interval

REASON: Increasing n = sample size decreases the Standard Error and the Width of the Condidence Interval is proportional to Standard Error.

(b)

The effect of increasing the size of a sample on the p-value of a test, when H0 is false:

Increasing the sample size = n will decrease the p-value if H0 is false. An effect that fails to be significant at a specified value of in a small sample can be significant in a larger sample.