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) \(- 0.0177 < p _ { 1 } - p _ { 2 } < 0.1243\)

---

Definitions:

Hedonic Adaptation

The observed process of becoming accustomed to a new situation or stimulus, causing the emotional effects of that stimulus to diminish over time.

Fancy Dinner

An elaborate or formal evening meal, often involving multiple courses and sophisticated cuisine.

Mood

A temporary state of mind or feeling that influences an individual's emotional state.

Slippery Slope

A logical fallacy or argument that suggests a small first step leads to a chain of related events culminating in a significant (usually negative) effect.