Question

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, 814 indicated that careless or aggressive driving was the biggest threat on the road. In addition, 440 respondents said cell phone usage by other drivers was the driving behavior that annoyed them the most.

a) Based on the data, construct and interpret a 95% confidence interval estimate for the true proportion in the population of all drivers who are annoyed by cell phone usage.

b) Construct and interpret a 98% confidence interval for the population proportion of all drivers who indicated that careless or aggressive driving was the biggest threat on the road.

c) For part (a), what sample size should be used if we want a 99% confidence interval within ±2%

Answer 1