Question

In 2008 the Better Business Bureau settled 70% ce complaints it received (USA Today, March 2, 2009), suppose you have been this year involving proportion of complaints settied for new car dealers is 0.7, the same as the overall proportion of complaints settled in 2008 Round your answers to four decimal places a. Suppose you select a sample of 450 complaints involving new car dewiers. Show the sampling d hired by the Better Business Bueau te invesigate the complaints t received new car dealers You pian to select a sample of new cer dealer complaints to estimate the propertion of complaints the Better Business Buresu is able to settle. Assume the population the sampling distribution of p The distribution is Mean Dased upon a sample of 450 complaints, what is the probabity that the sample proportion will be within 04 of the popuis b. Based upon a distribution of . In determining your answer, use the standard error found in part a. and the probability Suppose you select a sample of 200 complaints found using the tabies in the The distribution is GSelect-newer : 0 involving neค car dealers. Show the samping ofp.n Hean d. Based upon the smaller sample of only 200 compiaints, what is the probability that the sample proportion wil be within 04 of the population proportion e. As measured by the increase in probability, how much more precise is the result, when you use a sample of 450 instead of a sample of 200

Answer 1

a)the distribution is normal

mean =0.7

std error of proportion=σp=√(p*(1-p)/n)=

0.0216

b)

probability =

P(0.66<X<0.74)

=

P(-1.85<Z<1.85)=

0.9678-0.0322=

0.9356

c)

the distribution is normal

mean =0.7

std error of proportion=σp=√(p*(1-p)/n)=

0.0324

d)

probability =

P(0.66<X<0.74)

=

P(-1.23<Z<1.23)=

0.8907-0.1093=

0.7814

e) change = 0.9356-0.7814 =0.1542