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 1060 people randomly selected from their mailing list of over 200,000 people. They get orders from 118 of the recipients. Use this information to complete parts a through d. a) Create a 90% confidence interval for the percentage of people the company contacts who may buy something. (%, %) b) Explain what this interval means. A. The company is 90% confident that the percentage of people who will not respond to the flyer falls within the confidence interval bounds. B. The company is 90% confident that the percentage of people who will respond to the flyer falls within the confidence interval bounds. C. The values for the interval bounds should be subtracted from 90% to obtain the company's true confidence level. D. The company is 90% confident that the probability a randomly sampled person will respond to the flyer falls within the confidence interval bounds. c) Explain what "90% confidence" means. A. About 90% of all randomly sampled people will respond to the new flyer. B. About 90% of all random samples of size 1060 will produce intervals that do not contain the true proportion of people who will respond to the new flyer. C. About 90% of all random samples of size 1060 will produce intervals that contain the true proportion of people who will respond to the new flyer. D. About 90% of all random samples will produce intervals that contain the true proportion of people who will respond to the new flyer. d) The company must decide whether to do a mass mailing. The mailing won't be cost-effective unless it produces at least a 5% return. What does your confidence interval suggest? A. Do the mass mailing. B. Do not do the mass mailing.

Explanation / Answer

a) The statistical software output for 90% confidence interval will be:

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

90% confidence interval results:

Hence,

90% confidence interval will be:

(9.5%, 12.7%)

b) Option B is correct.

c) Option C is correct.

d) Since the 90% confidence interval contains value greater than 5%, do the mass mailing.

Option A is correct.

Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 118 1060 0.11132075 0.0096606791 0.095430352 0.12721116

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