AP Statistics / Unit 4: Inference for Quantitative Data: Means
4.10 Carrying Out a Test for the Difference Between Two Population Means
Notes
$$t=\frac{(\bar x_1-\bar x_2)-0}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$$
- Get the p-value with technology; compare with $\alpha$; conclude in context.
Practice
$\bar x_1-\bar x_2=4$ with standard error 2. $t=$
$\displaystyle \frac{4}{2}$.
A p-value of 0.01 with $\alpha=0.05$ means:
Reject $H_0$.
An observational study rejects $H_0$. We can conclude:
Without random assignment, no causation.
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