Final answer:
The margin of error for a 95% confidence interval based on a survey where 54 out of 120 adults purchased a flat screen television is calculated using a specific formula yielding a result of approximately 0.089. Option D is the correct answer.
Step-by-step explanation:
The student is asked to calculate the margin of error for a 95% confidence interval of the proportion of adults who have purchased a flat screen television, based on a survey of 120 adults at Walmart in which 54 reported having made such a purchase.
To calculate the margin of error, the following formula is used:
]Margin of Error = Z * sqrt((p*(1-p))/n)
where:
- Z is the z-score corresponding to the desired confidence level (1.96 for 95%)
- p is the sample proportion (54/120)
- n is the sample size (120)
Plugging in the values, we get:
Margin of Error = 1.96 * sqrt((0.45*(1-0.45))/120) = 1.96 * sqrt((0.45*0.55)/120) = 1.96 * sqrt(0.2475/120) = 1.96 * sqrt(0.0020625) = 1.96 * 0.0454 ≈ 0.089
Therefore, the correct answer is D. 0.089.