4.8 Justifying a Claim Based on a Confidence Interval for the Difference Between Two Population Means

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

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

• A confidence interval for the difference between two population means provides an interval of values that may serve as convincing evidence to support a particular claim about the difference in two population means. For example, if the interval contains 0, then there is insufficient evidence to conclude there is a difference between the two population means. If the interval does not contain 0, then there is sufficient evidence to conclude there is a difference between the two population means. 137 Inference for Quantitative Data: Means UNIT 4