Question

TicksLyme disease is spread in the northeastern United States by infected ticks. The ticks are infected mainly by feeding on mice, so more mice result in more infected ticks. The mouse population, in turn, rises and falls with the abundance of acorns, their favored food. Experimenters studied two similar forest areas in a year when the acorn crop failed. To see if mice are more likely to breed when there are more acorns, the researchers added hundreds of thousands of acorns to one area to imitate an abundant acorn crop, while leaving the other area untouched. The next spring, $54$of the $72$mice trapped in the first area were in breeding condition, versus $10$of the $17$mice trapped in the second area.

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 researched want to know that if population of mice with additional acorns that are in bleeding conditions larger than population of mice without additional acorns that are in breeding condition or not.

$x_1=54$

$x_2=10$

$n_1=72$

$n_2=17$

Appropriate Hypothesis

Claim is proportion is greater for mice in first area with the acorns.

Appropriate hypothesis is:

Null: $H_0:p_1=p_2$

Alternative: $H_a:p_1>p_2$

$p_1$is proportion of mice in an area with additional acorns that are in breeding conditions and $p_2$ is proportion of mice in an area without additional acorns that are in breeding conditions.

Conditions

The conditions are:

Random: The mice are already living in those forests before any treatments were given and thus the mice were not randomly selected nor randomly assigned to a treatment. It is not satisfied.

Independent: In first forest, $72<10\%$of all mice in first forest and $17<10\%$of all mice in second forest.

Normal: There are ten success and $7$failures which is less than $10$.

All conditions are not satisfied. We can't use hypothesis test.