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Answer:
Correct option: As the sample size decreases, the margin of error increases.
Step-by-step explanation:
The (1 - <em>α</em>) % confidence interval for population proportion is:
The margin of error in this confidence interval is:
The sample size <em>n</em> is inversely related to the margin of error.
An inverse relationship implies that when one increases the other decreases and vice versa.
In case of MOE also, when <em>n</em> is increased the MOE decreases and when <em>n</em> is decreased the MOE increases.
Compute the new margin of error for <em>n</em> = 125 as follows:
*Use <em>z</em>-table for the critical value.
For <em>n</em> = 125 the MOE is 0.086.
And for <em>n</em> = 275 the MOE was 0.058.
Thus, as the sample size decreases, the margin of error increases.