A common characterization of obese individuals is that their body mass index is at least 30 [BMI = weight/(height)2, where height is in meters and weight is in kilograms]. The article "The Impact of Obesity on Illness Absence and Productivity in an Industrial Population of Petrochemical Workers" (Annals of Epidemiology, 2008: 8-14) reported that in a sample of female workers, 262 had BMIs of less than 25, 159 had BMIs that were at least 25 but less than 30, and 120 had BMIs exceeding 30. Is there compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese?
a. State and test appropriate hypotheses with a significance level of .05.
b. Explain in the context of this scenario what constitutes type I and II errors.
c. What is the probability of not concluding that more than 20% of the population is obese when the actual percentage of obese individuals is 25%?