Question

Explain why the conditions for using two-sample z procedures to perform inference about $p1-p2$are not met in the settings

Shrubs and fire Fires are a serious threat to shrubs in dry climates. Some shrubs can resprout from their roots after their tops are destroyed. One study of resprouting took place in a dry area of Mexico.$7$The investigators randomly assigned shrubs to treatment and control groups. They clipped the tops of all the shrubs. They then applied a propane torch to the stumps of the treatment group to simulate a fire. All $12$of the shrubs in the treatment group were resprouted. Only $8$ of the $12$ shrubs in the control group were resprouted.

Short answer

From the given information, here, success in the treatment group is $8$which is less than $10$. It implies that the normality assumption is not fulfilled here.

So, the two-proportion z -test is not appropriate in this case.

Step-by-step solution

Given Information

It is given in the question that, for treatment group

Number of success $\left(x\right)=8$

Number of events$\left(n\right)=12$

Step 2: Explanation

To conduct the two-proportion z -test, the number of successes in both samples must be more than $10$. Here, success in the treatment group is $8$which is less than $10$. It implies that the normality assumption is not fulfilled here.

So, the two-proportion z -test is not appropriate in this case.