Question

A poll asked 1,060 adults if they would rate the quality of the environment in this country as "good." A total of 60% of the respondents replied "yes." What is the margin of error for a 94% confidence interval for the population proportion answering yes?

Answer 1

The answer to the question is

Margin of error = 2.83%

Explanation:

The margin of error is the central range about the mean which provide a description of how accurate a given statistics sample information is in relation to the actual population. It is the radius of confidence of a statistic.

Margin of error for a proportion is given by

`z*\sqrt{(\rho(1-\rho))/(n) }`

Where

ρ = Sample proportion

n = Sample size

z = z score, critical value at 94 % = 1.88

= 1.88*
`\sqrt{(0.6*0.4)/(1060) }` = +2.8×10⁻²

⇒

1.88×(0.6×0.4/1060)^0.5

= 0.0283

Converting to percentage gives 0.0283×100 = 2.83%

Margin of error = 2.83%