Construct the Indicated Confidence Interval for the Difference Between Population $0.0247 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.0286$

question 30

Multiple Choice

Construct the indicated confidence interval for the difference between population proportions p1 - p2. Assume that the samples are independent and that they have been randomly selected.
-A marketing survey involves product recognition in New York and California. Of 558 New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product. Construct a 99% confidence interval for the difference between the two population proportions.

• A) \(0.0247 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.0286\)
• B) \(- 0.0443 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.0976\)
• C) \(- 0.0034 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.0566\)
• D) \(- 0.0177 < p _ { 1 } - p _ { 2 } < 0.1243\)

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Definitions:

Catalog

A comprehensive collection or list of items, especially one systematically arranged, often found in printed form or online for shopping purposes.

Media Usage

The manner and extent to which individuals or organizations use various channels of communication to receive or disseminate information.

Demographics

Statistical data relating to the population and particular groups within it, often used for identifying marketing targets.

Direct Order

A method of purchasing where buyers directly contact the suppliers to place an order, eliminating intermediaries.