In 2016 the Better Business Bureau settled 80% of complaints they received in the United States. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.80, the same as the overall proportion of complaints settled in 2016. Required:
a. Based upon a sample of 220 complaints, what is the probability that the sample proportion will be within 0.04 of the population proportion? (Round your answer to four decimal places.)
b. Based upon the larger sample of 470 complaints, what is the probability that the sample proportion will be within 0.04 of the population proportion? (Round your answer to four decimal places.)
c. As measured by the increase in probability, how much do you gain in precision by taking the larger sample in part (a)?