Question

Direct mail advertisers send solicitations ("junk mail") to thousands of potential customers in the hope that some will buy the company's product. The response rate is usually quite low. Suppose a company wants to test the response to a new flyer and sends it to 1130 people randomly selected from their mailing list of oter 200,000 people. They get orders from 123 of the recipients. Use this information to complete parts a through d. a) Create a 95% confidence interval for the percentage of people the company contacts who may buy something (%%) (Round to one decimal place as needed.) b) Explain what this interval means. O A. The company is 95% confident that the percentage of people who will not respond to the flyer falls within the confidence interval bounds. B. The values for the interval bounds should be subtracted from 95% to obtain the company's true confidence level. O C. The company is 95% confident that the probability a randomly sampled person will respond to the flyer falls within the confidence interval bounds. OD. The company is 95% confident that the percentage of people who will respond to the flyer falls within the confidence interval bounds.

Answer 1

a)

sample success x =		123
sample size n=		1130.0
pt estiamte p̂ =x/n=		0.10885
se= √(p*(1-p)/n) =		0.0093
for 95 % CI value of z=		1.960	from excel:normsinv((1+0.95)/2)

margin of error E=z*std error   =		0.018
lower bound=p̂ -E                       =		0.091
Upper bound=p̂ +E                     =		0.127
from above 95% confidence interval for population proportion =(9.1 % ,12.7 %)

b)

O D. The company is 95% confident that the percentage of people who will respond to the flyer falls within the confidence interval bounds.

c)

C. About 95% of all random samples of size 1130 will produce intervals that contain the true proportion of people who will respond to the new flyer.

d)

Do the mass mailing (since interval values are above 5%)