Back to Inference for Quantitative Data: Means

Lesson PreviewLesson 7 of 9 in this unit

7.7 Justifying a Claim About the Difference of Two Means Based on a Confidence Interval

Part of Inference for Quantitative Data: Means in AP® Statistics. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

Start free

Interpreting a Two-Sample t CI

The same logic applies as in Unit 6:

If 0 is inside the CI for μ1−μ2{\mu_1 - \mu_2}:

  • No convincing evidence of a difference in means
  • Fail to reject H0:μ1=μ2{H_0: \mu_1 = \mu_2}

If CI is entirely positive:

  • Evidence that μ1>μ2{\mu_1 > \mu_2}

If CI is entirely negative:

  • Evidence that μ1<μ2{\mu_1 < \mu_2}

Key questions when interpreting:

  1. Does the interval include 0?
  2. What do the signs of the bounds tell us about the direction of the difference?
  3. How large is the difference practically (not just statistically)?

Statistical vs. practical significance: A CI can show a statistically significant difference (0∉{0 \notin} CI) but a tiny interval — a practically unimportant difference. Always consider the magnitude of the difference alongside whether it's significant.

In this unit

9 lessons

  1. 7.1Introducing Statistics: Why Should I Worry About Error?Preview lesson
  2. 7.2Constructing a Confidence Interval for a Population MeanPreview lesson
  3. 7.3Justifying a Claim About a Population Mean Based on a Confidence IntervalPreview lesson
  4. 7.4Setting Up a Test for a Population MeanPreview lesson
  5. 7.5Carrying Out a Test for a Population MeanPreview lesson
  6. 7.6Confidence Intervals for the Difference of Two MeansPreview lesson
  7. 7.7Justifying a Claim About the Difference of Two Means Based on a Confidence IntervalThis lesson
  8. 7.8Setting Up a Test for the Difference of Two Population MeansPreview lesson
  9. 7.9Carrying Out a Test for the Difference of Two Population MeansPreview lesson

Continue the full lesson in Stellar

Create a free account to unlock the remaining sections, checkpoints, course practice, and progress tracking for AP® Statistics.

Start free