Question

Direct mail advisors send notifications to thousands of potential customers in the hope that summer by the company's product. The response rate is usually quite low. Suppose a company wants to test the response to a new flyer and send it to 1060 people randomly selected from their mailing list of over 200,000 people. They get orders from 110 of those people.

A) Create a confidence interval for the percentage of people to company contracts
who may buy something

Answer 1

Create a 90% confidence interval for the percentage of people the company contacts who may buy something.

Answer:

CI = (8.84%, 11.92%)

We are 90% Confident that the percentage of people the company contacts who may buy something is between 8.84% and 11.92%.

Explanation:

We are given;

n = 1060

x = 110

Confidence level = 90%

Sample proportion; p^ = x/n = 110/1060

p^ = 0.1038

DF = n - 1 = 1060 - 1 = 1059

From the table attached, the critical value for a confidence level of 90% at a DF greater than 1000 is 1.645

Formula for CI is;

CI = p^ ± t√(p^(1 - p^)/n)

CI = 0.1038 ± 1.645√(0.1038(1 - 0.1038)/1060)

CI = 0.1038 ± 0.0154

CI = (0.0884, 0.1192) or

CI = (8.84%, 11.92%)

Thus, we are 90% Confident that the percentage of people the company contacts who may buy something is between 8.84% and 11.92%.