Question

1. a scientist selects 20 ladybugs, then divides them by a random process into two groups. one group will be placed in a container near an insect repellant and the scientist will measure their speed of moving away from the repellant in the container. the second group will be placed in an empty container and the scientist will measure their speed of movement in the container.

a. why is it important that the scientist divides the ladybugs into two groups at random?
b. the scientist finds that the mean speed for the ladybugs moving away from the repellant is 22.16 kilometers per hour. the mean speed for the ladybugs moving in the empty container is 10.66 kilometers per hour. the scientist does a simulation and examines the resulting randomization distribution. does the repellant have an effect on the ladybug movement speed, or is random assignment to groups a reasonable explanation for the difference? explain your reasoning.

Explanation:

a. Random division helps to create two comparable groups. It reduces the impact of pre - existing differences among ladybugs (such as natural speed variations) so that any observed difference in speed can be more likely attributed to the presence of the repellent rather than other factors.
b. The mean speed of ladybugs near the repellent (22.16 km/h) is much higher than those in the empty container (10.66 km/h). Looking at the randomization distribution graph, if the differences in means around 0 are common and the observed difference is far from 0, it is unlikely that the difference is due to random assignment. So, the repellent likely has an effect on ladybug movement speed. The observed difference in means is large and not typical in the randomization distribution, suggesting a real effect of the repellent.

Answer:

a. To control for pre - existing differences among ladybugs and make the groups comparable for a valid test of the repellent's effect.
b. The repellent likely has an effect. The large difference in mean speeds (22.16 km/h vs 10.66 km/h) and the position of this difference relative to the randomization distribution suggest it is not due to random assignment.