solution

On the trail of the cockroach. Knowledge of how cockroaches forage for food is valuable for companies that develop and manufacture roach bait and traps. Many entomologists believe, however, that the navigational behavior of cockroaches scavenging for food is random. D. Miller of Virginia Tech University challenged the “random-walk” theory by designing an experiment to test a cockroach’s ability to follow a trail of their fecal material (Explore, Research at the University of Florida, Fall 1998).
A methanol extract from roach feces—called a pheromone—was used to create a chemical trail. German cockroaches were released at the beginning of the trail, one at a time, and a video surveillance camera was used to monitor the roach's movements. In addition to the trail containing the fecal extract (the treatment), a trail using methanol only (the control) was created. To determine if trail-following ability differed among cockroaches of different age, sex, and reproductive status, four roach groups were used in the experiment: adult males, adult females, gravid (pregnant) females, and nymphs (immatures). Twenty roaches of each type were randomly assigned to the treatment trail, and 10 of each type were randomly assigned to the control trail. Thus, a total of 120 roaches were used in the experiment. The movement pattern of each cockroach was measured (in “pixels”) as the average trail deviation. The data for the 120 cockroaches in the study are stored in the accompanying file. (The first 5 and last 5 observations in the data set are listed here.) Conduct a complete analysis of the data. Determine whether roaches can distinguish between the fecal extract and control trail and whether trail-following ability differs according to age, sex, and reproductive status.