Chapter 4.3, Problem 100E

(a)

To determine

To calculate the difference (Ivermectin minus Malathion) in the proportionof household that were free from head lice in the two groups.

Answer to Problem 100E

  $0.1337$ is the difference in the proportion of the two medicines.

Explanation of Solution

A study was conducted to see the difference in the two medicine used to treat the head lice. First medicine Ivermectin was used which shows $171\text{ out of 185}$ households were free from head lice and second medicine called Malathion shows that $151\text{ out of 191}$ households were free from head lice.

Thus the difference in the proportion of the two medicines can be calculated as:

Proportion of Ivermectin minus Proportion ofMalathion.

Thus, we have:

  $\begin{array}{l}=\frac{171}{185}-\frac{151}{191}\\ =0.9243-0.7906\\ =0.1337\end{array}$

Thus, we have $0.1337$ is the difference in the proportion of the two medicines.

(b)

To determine

To explain what does the dot $0.09$ means in this context.

Explanation of Solution

The dot $0.09$ means thatit is an outlier in the dot plot of the difference in proportion of the two medicines. This means that there is very few chances that there will be larger difference in the proportion of the two medicines that treated the head lice from different households.

(c)

To determine

To use the result of the simulation to find out if the difference in proportion from part (a) is statistically significant or not and explain.

Explanation of Solution

The difference in proportion from part (a) is statistically significant as the study is deemed statistically significant if there's a very low probability the result could have occurred by chance. And the result in the difference of proportion calculated in part (a) is very less so we can say that it is statistically significant as there is very less probability that the result has occurred by chance.