In 2008 the Better Business Bureau settled 75% of complaints they received (uSa today,March 2, 2009). 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 asample of new car dealer complaints to estimate the proportion of complaints the BetterBusiness Bureau is able to settle. Assume the population proportion of complaints settledfor new car dealers is .75, the same as the overall proportion of complaints settled in 2008.a. Suppose you select a sample of 450 complaints involving new car dealers. Show thesampling distribution of p.b. Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion?c. Suppose you select a sample of 200 complaints involving new car dealers. Show thesampling distribution of p.d. Based upon the smaller sample of only 200 complaints, what is the probability that thesample proportion will be within .04 of the population proportion?e. As measured by the increase in probability, how much do you gain in precision bytaking the larger sample in part (b)?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
In 2008 the Better Business Bureau settled 75% of complaints they received (uSa today,
March 2, 2009). 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 .75, the same as the overall proportion of complaints settled in 2008.
a. Suppose you select a sample of 450 complaints involving new car dealers. Show the
sampling distribution of p.
b. Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion?
c. Suppose you select a sample of 200 complaints involving new car dealers. Show the
sampling distribution of p.
d. Based upon the smaller sample of only 200 complaints, what is the probability that the
sample proportion will be within .04 of the population proportion?
e. As measured by the increase in probability, how much do you gain in precision by
taking the larger sample in part (b)?
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