Question

lesson 4.7 / hw
a study published in the new england journal of medicine compared two medicines to treat head lice: an oral medication called ivermectin and a topical lotion containing malathion. researchers studied 812 people in 376 households in seven areas around the world. of the 185 households randomly assigned to ivermectin, 171 were free from head lice after 2 weeks, compared with only 151 of the 191 households randomly assigned to malathion.
one hundred trials of a simulation were performed to see what differences in proportions would occur due only to chance variation in the random assignment, assuming that the type of medication doesnt matter. the results are shown in the dotplot.
dotplot image: x-axis labeled simulated difference (ivermectin - malathion) in proportion who were free from head lice with values from -0.08 to 0.08, y-axis with dots representing frequency
use the results of the simulation to determine if the difference in proportions of 0.13 is statistically significant. explain your reasoning.
options:

• because a difference of proportions of 0.13 or higher never occurred in the simulation, the difference is not statistically significant. it is quite plausible to get a difference this big simply due to chance variation in the random assignment.
• because a difference of proportions of 0.13 or higher occurred 4 out of 100 times in the simulation, the difference is statistically significant. it is extremely unlikely to get a difference this big simply due to chance variation in the random assignment.
• because a difference of proportions of 0.13 or higher occurred 18 out of 100 times in the simulation, the difference is not statistically significant. it is quite plausible to get a difference this big simply due to chance variation in the random assignment.
• because a difference of proportions of 0.13 or higher never occurred in the simulation, the difference is statistically significant. it is extremely unlikely to get a difference this big simply due to chance variation in the random assignment.
• according to the results of the simulation, the distribution is approximately normal, so the data is statistically significant.

Explanation:

To determine statistical significance, we check how often a difference of 0.13 (or higher) occurs in the simulation. If it occurs rarely (low frequency), the difference is significant (unlikely due to chance). If it occurs often, it's not significant (plausible due to chance).

Looking at the options:

• The correct reasoning is that if a difference of 0.13 or higher occurred 4 out of 100 times (low frequency, 4% chance), it's extremely unlikely to be due to chance, so the difference is statistically significant. This matches the second option's logic: "Because a difference of proportions of 0.13 or higher occurred 4 out of 100 times in the simulation, the difference is statistically significant. It is extremely unlikely to get a difference this big simply due to chance variation in the random assignment."

Answer:

B. Because a difference of proportions of 0.13 or higher occurred 4 out of 100 times in the simulation, the difference is statistically significant. It is extremely unlikely to get a difference this big simply due to chance variation in the random assignment.