Changes in the Margin of Error: Suppose you are constructing confidence interval

Question

Changes in the Margin of Error: Suppose you are constructing confidence intervals about a mean or proportion. Answer the following questions about the margin of error (E) when the following changes are made.

(a) If the confidence level decreases, then which of the following is true? the margin of error will decrease the margin of error should not change the margin of error will increase

(b) If the sample size gets smaller while the confidence level and sample statistics remain constant, then which of the following is true? the margin of error will decrease the margin of error should not change the margin of error will increase

Explanation / Answer

Margin of Error = (critical value) * (standard error)

(a) If the confidence level decreases, the margin of error will decrease. Because margin of error depends upon the critical value, and critical value is depends on level of confidence interval.

for example if we calculate 99% confidence interval for population mean. Population standard deviation is known, then the Z-critical value is 2.33. And if we calculate 95% confidence interval for population mean. Population standard deviation is known, Z-critical value is 1.645.

Observed that if we decrease the level of CI critical value also decrease and simultaneously margin of error also decreases.

(b) If the sample size gets smaller while the confidence level and sample statistics remain constant, then margin of error will increase.

Margin of error is also depends on standard error (SE). Suppose we calculate CI for population mean then the standard error SE = standard deviation/sqrt(n), and if sample size n gets smaller the SE is increases. simultaneously margin of error also increases.

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