3.11 Justifying a Claim Based on a Confidence Interval for the Difference Between Two Population Proportions

Interpret a confidence interval in context for the difference between two population proportions.

• Because the confidence interval for the difference between two population proportions is calculated based on samples from two populations, the computed interval may or may not contain the value for the difference between those two population proportions.
• The interpretation of the confidence level is as follows: In repeated random sampling with the same sample sizes from the same populations, approximately C% of confidence intervals created will capture the difference between the two population proportions, where C represents the numerical value of the confidence level used.
• When interpreting a C% confidence interval for the difference between two population proportions, we say we are C% confident that the interval ab, contains the parameter for the difference between the populations, where a represents the lower limit and b represents the upper limit. An interpretation of a confidence interval for the difference between two population proportions includes a reference to the parameter with the details about the populations it represents in the context of the study.

Justify a claim based on a confidence interval for the difference between two population proportions.

• A confidence interval for the difference between two population proportions provides an interval of values that may provide convincing evidence to support a particular claim about the difference between the two population proportions. For example, if the interval contains 0, then there is insufficient evidence to conclude there is a difference between the two population proportions. If the interval does not contain 0, there is sufficient evidence to conclude there is a difference between the two population proportions. Inference for Categorical Data: Proportions UNIT 3 106