3. Provide answers to the following: (a) In a survey of a simple random sample of 100 patients, a researcher finds that 55 of the patients gave the rating of less than 2.0 for food served during their hospital stay. Construct a 90 percent confidence interval for T, the population proportion of patients who rated the food at less than 2.0. (8 ) (b) To limit the spread of a certain virus, all residential areas had to provide the size of families per household to be recorded. The management of a private condominium reported that 37 percent of the residents of the condominium had more than 4 family members living with them. A random sample of 100 residents at the condominium were selected and it showed that 23 residents had more than 4 family members with them. At a = 0.01, is there enough evidence that the percentages have changed? [ All work must be shown] ( 12 )