AP Statistics / Unit 4: Inference for Quantitative Data: Means
4.5 Carrying Out a Test for a Population Mean or Population Mean Difference
Notes
$$t=\frac{\bar x-\mu_0}{s/\sqrt n},\quad df=n-1$$
- Find the p-value from the $t$ distribution, compare with $\alpha$, and conclude in context.
Practice
$\bar x=52$, $\mu_0=50$, $s=8$, $n=16$. $t=$
$\displaystyle \frac{2}{8/4}$.
For the same $t$ with a larger $n$ (same $\bar x$ and $s$), the $t$ statistic:
The standard error shrinks.
p-value 0.30, $\alpha=0.05$. Conclusion:
Large p-value.
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