Question

Shrubs and fire Fire is a serious threat to shrubs in dry climates. Some shrubs can

resprout from their roots after their tops are destroyed. Researchers wondered if fire would help with resprouting. One study of resprouting took place in a dry area of Mexico. The researchers 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 resprouted. Only $8$of the $12$shrubs in the control group resprouted.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.

Short answer

a. The hypothesis are $H_0:p_1=p_2$and $H_a:p_1>p_2$

b. All conditions are not met.

Step-by-step solution

Given Information

It is given that the researchers want to know that if there is a difference in the proportion of shrubs that received the treatment and resprouted and the shrubs that did not received the treatment and resprouted.

$x_1=12$

$x_2=8$

$n_1=12$

$n_2=12$

Appropriate hypothesis

Claim is that proportion is greater than shrubs in treatment group.

The appropriate hypothesis is:

Null: $H_0:p_1=p_2$

Alternative: $H_a:p_1>p_2$

$p_1$is proportion of shrubs that received the treatment and resprouted.

$p_2$is proportion of shrubs that did not received the treatment and resprouted.

Conditions

Three conditions are:

Random: Independent random samples assigned to shrubs.

Independent: $12$shrubs is less than $10\%$of all shrubs.

Normal: There are $12$success and zero failures, zero is less than ten.

All conditions are not satisfied. We cannot use hypothesis for testing a claim.