You are testing a hypothesis that population density of a particular plant species influences the rate at which a pathogenic fungus infects the plant. Because the fungus causes visible scars on the leaves, you can easily determine whether a plant is infected. Design an experiment to test your hypothesis. Include your experimental treatments and control, the data you will collect, and the results expected if your hypothesis is correct.

To design an experiment to test the hypothesis that population density of a particular plant species influences the rate at which a pathogenic fungus infects the plant, here are the steps you can follow:

1. Experimental treatments: Identify a sample group of plants from the same species. Divide the plants into different treatment groups with varying population densities. For example, you can have treatment groups with low, medium, and high population densities.

2. Control group: Create a control group with plants having a standard or natural population density. This group will help you compare the infection rate against the different treatment groups.

3. Randomization: Randomly assign the plants to the treatment and control groups. This helps to ensure that any differences observed are not due to a specific plant characteristic but rather the population density.

4. Measurement and data collection: Determine a set duration for the experiment. Regularly monitor and record the number of infected plants and the severity of infection in each group. You can do this by visually inspecting the leaves and quantifying the number and size of fungal scars.

5. Statistical analysis: After collecting data, perform statistical analysis (e.g., chi-square test, analysis of variance) to identify any significant differences in the infection rates between the treatment and control groups.

6. Results expectation: If the hypothesis is correct, you would expect to observe a correlation between population density and the infection rate of the pathogenic fungus. Specifically, you might expect to see a higher infection rate in the treatment groups with higher population densities compared to the control group.

Remember that experiments should be conducted multiple times for statistical validity. Moreover, controlling for other variables such as nutrition, moisture, and sunlight is crucial to ensure that any observed differences are primarily due to population density's impact on the infection rate.