Chapter 5, Problem 85E

Suppose the hypothetical data below are from a toxicity study designed to measure the effectiveness of different doses of a pesticide on mosquitoes. The table below summarizes the concentration of the pesticide, the sample sizes, and the number of mosquitoes killed.

1. a. Make a scatterplot of the proportions of mosquitoes killed versus the pesticide concentration.
2. b. Using the techniques introduced in this section, calculate $y^{\prime }=\ln \left(\frac{p}{1-p}\right)$ for each of the concentrations and fit the line y′ = a + b (Concentration). What is the significance of a positive slope for this line?
3. c. The point at which the dose kills 50% of the mosquitoes is sometimes called LD50, for “Lethal dose 50%.” What would you estimate LD50 to be for this pesticide when used on mosquitoes?