In 2010 the Better Business Bureau settled 80% of complaints they received. 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 .80, the same as the overall proportion of complaints settled in 2010.
a) Suppose you select a sample of 500 complaints involving new car dealers. Show the sampling distribution of "p bar". (Calculate Mean and Standard Deviation)
b) Based upon a sample of 500 complaints, what is the probability that the sample proportion will be within .05 of the population proportion?
c) Suppose you select a sample of 250 complaints involving new car dealers. Show the sampling distribution of "p bar". (Calculate Mean and Standard Deviation)
d) Based upon the smaller sample of only 250 complaints, what is the probability that the sample proportion will be within .05 of the population proportion?