Direct mail advertisers send solicitations (\"junk mail\") to thousands of poten

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 1200 people randomly selected from their mailing list of over 200,000 people. They get orders from 130 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.

left parenthesis nothing % comma nothing % right parenthesis9.

?%, ?%

(Round to one decimal place as needed.)

b) Explain what this interval means.

A. The company is 95% confident that the probability a randomly sampled person will respond to the flyer falls within the confidence interval bounds.

B. The company is 95% confident that the percentage of people who will not respond to the flyer falls within the confidence interval bounds

C. The values for the interval bounds should be subtracted from 95% to obtain the company's true confidence level.

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

c) Explain what "95% confidence" means.

A. About 95% of all random samples of size 1200 will produce intervals that contain the true proportion of people who will respond to the new flyer.Your answer is correct.

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

C. About 95% of all random samples of size 1200 will produce intervals that do not contain the true proportion of people who will respond to the new flyer.

D. About 95% of all randomly sampled people will respond to the new flyer.d)

d) The company must decide whether to do a mass mailing. The mailing won't be cost-effective unless it produces at least a 4% return. What does your confidence interval suggest?

A. Do not do the mass mailing.

B. Do the mass mailing.

Explanation / Answer

The statistical software output for 95% confidence interval is:

One sample proportion confidence interval:
p : Proportion of successes
Method: Standard-Wald

95% confidence interval results:

Hence,

95% confidence interval will be:

(9.1%, 12.6%)

b) Option D is correct.

c) Option A is correct.

d) Option B is correct.

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