9.38 Bacteria in water samples are sometimes difficult to count, but their presence can easily be detected by culturing. In 50 independently selected water samples from a certain lake, 43 contained certain harmful bacteria. After adding a chemical to the lake water, another 50 water samples showed only 22 with the harmful bacteria. Estimate the true difference between the proportions of samples containing the harmful bacteria, with a 95% confidence coefficient. Does the chemical appear to be effective in reducing the amount of bacteria?