3.4.C—Identify the relationships among sample size, confidence interval width, confidence level, and margin of error…

Identify the relationships among sample size, confidence interval width, confidence level, and margin of error for a population proportion.

• For a given sample, increasing the confidence level will result in the following:
  • i. The critical value will increase.
  • ii. The margin of error will increase.
  • iii. The width of the confidence interval will increase.
• Increasing the sample size decreases the standard error. Thus, when all other things remain the same, the width of the confidence interval for a population proportion tends to decrease as the sample size increases. For a confidence interval for a population proportion with a given confidence level, the width of the interval is approximately proportional to 1 n . Inference for Categorical Data: Proportions UNIT 3 92