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 1,500 randomly selected people. The company gets orders from 109 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.

The company is​ 95% confident that the proportion of people who may buy something is between ?% and ?​%.

Answer 1

Total number of sample (n) = 1500
number of favourable events (X) = 109
Sample proportion = 0.0727
Sample size (n) = 1500
Confidence interval(in %) = 95
z @ 95% = 1.96
Since we know that

Required confidence interval = (0.0727-0.0131, 0.0727+0.0131)
Required confidence interval = (0.0596, 0.0858)
Please hit thumps up if the answer helped you.