Question

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:
1. Increases
2. Decreases
3. Unaffected
A. The margin of error of a 95% confidence interval.
B. The P-value of a test, when H0 is false and all facts about the population remain unchanged as n increases.
C. The power of a fixed level test when the alternative hypothesis, and all facts about the population remain unchanged.

Answer 1

Answer:

Margin of Error decreases

Pvalue decreases

Power increases

Step-by-step explanation:

The margin of error decreases as sample size increases given the same level of confidence, hence, the interval gets narrower.

The margin of error = (Zcritical * σ/√n) ; where, n is the denominator, as the denomination increases, the obtained value will decrease, hence, the margin of error.

When we have a false H0, then we expect a statistical result which will reject H0, with all facts remaining unchanged , increase in sample size n, will lead to decrease in Pvalue, because a lower P value increases the significance of statistical test needed to reject H0.

The power of a fixed level test when the null hypothesis is true, higher power is required to reject the null , increasing n will increase the probability of rejecting H0, by increasing the power of a fixed level test.