Question
9. Statisticians prefer large samples. Describe briefly the effect of increasing the size of a sample...
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.
Homework Answers
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.
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