7. Hypothesis Testing: Hypothesis Test for a Population Proportion
Hypothesis Test for a Proportion and Confidence Intervals
If you compute a #96\%\,CI# for #\pi# using
\[CI_{\pi}=\bigg(\hat{p}- z^*\cdot \sqrt{\cfrac{\pi_0\cdot(1-\pi_0)}{n}},\,\,\,\, \hat{p} + z^*\cdot \sqrt{\cfrac{\pi_0\cdot(1-\pi_0)}{n}} \bigg)\]
Then there exists a direct connection between a two-sided hypothesis test for #\pi# at the #\alpha = 0.04# level of significance and the confidence interval:
- If #\pi_0# falls the #96\%\,CI# then the null hypothesis #H_0# is rejected.
- If #\pi_0# falls the #96\%\,CI# then the null hypothesis #H_0# is not rejected.
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