The better business bureau settled 80% of complaints they received in 2012. suppose you have been hired by the better business bureau to investigate the complaints they received this year involving new card dealers. you plan to select a sample of new car dealer complaints to estimate the proportion of complaints the better bureau is able to settle. Assume the population proportion of complaints settled for her car dealers is 80%, the same as the overall proportion of complaints settled in 2012.
1) suppose you take a sample of 500 complaints involving new car dealers. what is the sampling distribution of the sample proportion?
2) what is the probability that at least 375 of the 500 complaints will be settled this year?
3)based on a sample of 500 complaints, what is the probability that the sample proportion would be within +/- 0.04 of the population proportion?
4)suppose you use a sample of 250, what is the probability that the sample proportion would be within +/-0.04 of the population proportion?
5) as measured by the increase in probability, how much do you gain in precision by taking the large sample in part 3) ?