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We are given that the first medicine, Ivermectin, was used and shows$171$out of$185$were free from head lice. Therefore, the proportion of Ivermectin$=\frac{171}{185}$

Second Medicine Malathion shows that$151$out of$191$was free from head lice

Therefore, the proportion of malathion$=\frac{151}{191}$

The difference in the proportions of the two medicines is: proportion of Ivermectin - Proportion of Malathion.

We have, difference=$\frac{171}{185}-\frac{151}{191}$

On solving, we get a difference.$=0.1337$

Hence, $0.1337$the difference in the proportion of households that were free from head lice in the two groups.

We are given the values of researchers' experiment randomly assigned to ivermectin and some were assigned to head lice and compared with malathion and we have to find out the significance of dot structure.

The dot$0.09$ signifies that the chances are very small that the difference in the proportion of the two medicines is larger.

We are given the values of researchers' experiments randomly assigned to ivermectin; some were assigned to head lice and compared with malathion and we have to find out if the result in part (a) is statistically significant or not.

Using the results of the simulation to determine if the difference in proportions from part (a) is statistically significant, we conclude that the difference is quite significant statistically only if there is low probability that results have occurred by chance. Also the difference is less which depicts that probability of result by chance is less.