Direct mail advertisers send solicitations (junk mail) to thousands of potential

Question

Direct mail advertisers send solicitations (junk mail) to thousands of potential customers hoping 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 1000 randomly selected people. The company gets orders from 139 of the recipients and decides to do a mass mailing list to everyone on its mailing list of over 200,000. Create a 95% confidence interval for the percentage of those people who will order something. (Use 1.96 for the z statistic)

Explanation / Answer

                                                                                           x                    =   117 sample size n                    = 1500 sample proportion     p x/n= 0.0780 std error       =Se            =(p*(1-p)/n) = 0.0069 for 95 % CI value of z= 1.9600 margin of error E=z*std error                            = 0.0136 lower confidence bound=sample proportion-margin of error 0.064 Upper confidence bound=sample proportion+margin of error 0.092

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