N. Hill et al. conducted a clinical study to compare the standard treatment for head lice infestation with the Bug Buster kit, which involves using a fine-toothed comb on thoroughly wet hair four times at 4-day intervals. The researchers published their findings in the paper “Single Blind, Randomised, Comparative Study of the Bug Buster Kit and over the Counter Pediculicide Treatments against Head Lice in the United Kingdom” (British Medical Journal, (Vol. 331, pp. 384–387). For the study, 56 patients were randomly assigned to use the Bug Buster kit and 70 were assigned to use the standard treatment. Thirty-two patients in the Bug Buster kit group were cured, whereas nine of those in the standard treatment group were cured.
a. At the 5% significance level, do these data provide sufficient evidence to conclude that a difference exists in the cure rates of the two types of treatment?
b. Determine a 95% confidence interval for the difference in cure rates for the two types of treatment.