7.5 Carrying Out 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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Computing the p-Value for a t-Test

Finding the p-value:

Right-tailed ( ${H_a: \mu > \mu_0}$ ): ${p = P(t_{df} \geq t_{obs})}$
Left-tailed ( ${H_a: \mu < \mu_0}$ ): ${p = P(t_{df} \leq t_{obs})}$
Two-tailed ( ${H_a: \mu \neq \mu_0}$ ): ${p = 2 \cdot P(t_{df} \geq |t_{obs}|)}$

On a TI calculator: tcdf(lower, upper, df)

Example: ${t_{obs} = 2.31}$ , ${df = 24}$ , right-tailed: p = P(t₂₄ ≥ 2.31) = tcdf(2.31, 999, 24) ${\approx 0.015}$

Example: ${t_{obs} = -1.80}$ , ${df = 15}$ , two-tailed: ${p = 2 \cdot P(t_{15} \leq -1.80) = 2 \cdot}$ tcdf(-999, -1.80, 15) ${\approx 2(0.046) = 0.092}$

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