Problem:
As the automobile accident rate increases, insurers are forced to increase their premium rates. Companies such as Allstate have recently been running a campaign they hope will result in fewer accidents by their policyholders. For each six-month period that a customer goes without an accident, Allstate will reduce the customer's premium rate by a certain percentage. Companies like Allstate have reason to be concerned about driving habits, based on a survey conducted by Drive for Life, a safety group sponsored by Volvo of North America, in which 1,100 drivers were surveyed. Among those surveyed, 74% said that careless or aggressive driving was the biggest threat on the road. One-third of the respondents said that cell phone usage by other drivers was the driving behavior that annoyed them the most.
Required:
Based on these data, assuming that the sample was a simple random sample, construct and interpret a 95% confidence interval estimate for the true proportion in the population of all drivers who are annoyed by cell phone users.
Explain the solution in detail.