3.4 Justifying a Claim Based on a Confidence Interval for a Population Proportion

Interpret a confidence interval in context for a population proportion.

• Because the confidence interval for a population proportion is calculated based on a sample from a population, the computed interval may or may not contain the value of the population proportion.
• The interpretation of the confidence level is that in repeated random sampling with the same sample size, approximately C% of confidence intervals calculated will capture the population proportion, with C representing the numerical value of the confidence level used.
• When interpreting a C% confidence interval for a population proportion, we say we are C% confident that the interval (,ab ) contains the true value of the parameter for the population, where a represents the lower limit and b represents the upper limit. An interpretation of a confidence interval for a population proportion includes a reference to the parameter with details about the population it represents in the context of the study.

Justify a claim based on a confidence interval for a population proportion.

• A confidence interval for a population proportion provides a range of plausible values that may serve as convincing evidence to support a particular claim about the population proportion. Inference for Categorical Data: Proportions UNIT 3

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