11.5 Confidence interval approach to hypothesis testing

In the preceding tutorial, we calculated the Agresti-Coull 95% confidence interval for the proportion of damsefly battles flown in the counter-clockwise direction as: 0.631 \(< {p} <\) 0.956.

Given that the interval excludes (does not encompass) the null hypothesized proportion of \(p_0 = 0.5\), we can reject the null hypothesis.

In this case, the appropriate concluding statement would be:

Counter-clockwise battles occurred in a significantly higher proportion than 0.5 (observed proportion of counter-clockwise battles = 0.85; Agresti-Coull 95% confidence interval: 0.631 < \({p}\) < 0.956.

  1. Binomial hypothesis test practice: Using the present tutorial as a guide, use a binomial test to address the question posed in Example 6.2 in the text book (concerning handedness in toads). Be sure to include all the steps of a hypothesis test.