Find the margin of error for the survey results described.
In a of 433 adults, 46% said that they favored the proposed environmental laws. Give your answer as a decimal to three decimal places
The margin of error can be calculated using the formula:
Margin of Error = Critical Value * Standard Error
The critical value corresponds to the level of confidence desired for the survey. Let's assume a 95% confidence level, which corresponds to a critical value of approximately 1.96 (which can be found in a standard normal distribution table).
The standard error can be calculated using the formula:
Standard Error = √(p(1-p)/n)
Where p is the proportion of adults favoring the proposed environmental laws (46% or 0.46), and n is the sample size (433).
Plugging in the values:
Standard Error = √(0.46(1-0.46)/433)
Standard Error = √(0.2492/433)
Standard Error ≈ 0.0171
Now, let's calculate the margin of error:
Margin of Error = 1.96 * 0.0171 ≈ 0.0335
Therefore, the margin of error for the survey results is approximately 0.033.