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7.4 Setting Up a Test 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-Test Setup

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

Hypotheses:

  • H0:μ=μ0{H_0: \mu = \mu_0} (a specific claimed value)
  • Ha:μ>μ0{H_a: \mu > \mu_0} (right-tailed)
  • Ha:μ<μ0{H_a: \mu < \mu_0} (left-tailed)
  • Ha:μ≠μ0{H_a: \mu \neq \mu_0} (two-tailed)

Conditions (same as CI):

  1. Random: random sample or randomized experiment
  2. Independence / 10% condition
  3. Normal / Large Sample:
    • n≥30{n \geq 30}: safe to proceed (CLT)
    • n<30{n < 30}: check for approximate normality — no strong skewness, no outliers
Test Statistic:
t=xˉ−μ0s/ndf=n−1t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}} \quad df = n-1

Then find the p{p}-value using the t{t}-distribution with df=n−1{df = n-1}.

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 MeanThis 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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