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7.2 Constructing a Confidence Interval for a Population Mean

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.

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One-Sample t Confidence Interval

Parameter: μ{\mu} = true mean of [population]

Conditions:

  1. Random: Random sample or randomized experiment
  2. Independence / 10% condition: n<10%{n < 10\%} of population
  3. Normal / Large Sample:
    • If n≥30{n \geq 30}: CLT guarantees approximate normality of Xˉ{\bar{X}} (use t regardless)
    • If n<30{n < 30}: The population must be approximately normal (no strong skewness, no outliers). Check with a dotplot, histogram, or Normal probability plot.
Formula:
xˉ±t∗⋅sn\bar{x} \pm t^* \cdot \frac{s}{\sqrt{n}}

where t∗{t^*} has degrees of freedom df=n−1{df = n - 1} and matches the desired confidence level.

Note: The margin of error is ME=t∗⋅(s/n){ME = t^* \cdot (s/\sqrt{n})}

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 MeanThis 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 IntervalPreview 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

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