In 2016 the Better Business Bureau settled 84% of complaints they received in the United States. Suppose you have
new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints t
car dealers is 0.84, the same as the overall proportion of complaints settled in 2016. Use the z-table.
a. Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of p.
E(p)
.84 (to 2 decimals)
=
.0259 (to 4 decimals)
b. Based upon a sample of 200 complaints, what is the probability that the sample proportion will be within 0.06 of t
probability = 1.5430
c. Suppose you select a sample of 460 complaints involving new car dealers. Show the sampling distribution of p.
E(p) =
.84 (to 2 decimals)
Op = .0170 (to 4 decimals)
d. Based upon the larger sample of 460 complaints, what is the probability that the sample proportion will be within
probability = .0170
e. As measured by the increase in probability, how much do you gain in precision by taking the larger sample in part
The probability of the sample proportion being within 0.06 of the population mean is increased by .135 (to 3 decimal points).