Sacktor et al. (2000) measured the neuropsychological performance of 33 HIV-positive patients undergoing antiretroviral therapy. Hand-use performance improved in 23 of the 33 patients but deteriorated in the remaining 10 patients. The graph below shows the log likelihood curve for the population proportion p of patients whose hand-use performance improved after antiretroviral therapy.

a. Using only the information in the log-likelihood curve, test the null hypothesis that the probability p is 0.5 using the log-likelihood ratio test.

b. Using the same curve, provide an approximate 95% confidence interval for the proportion of patients improving in the population.

Transcribed Image Text:

Log-likelihood -2 -4 -6 -8 -10 -12 0.3 0.4 0.5 0.6 0.7 0.8 Probability of improvement, p 0.9