Final answer:
The margin of error at a 95% confidence level for n = 490 and P Hat = 0.43 is 0.044 when rounded to three decimal places.
Step-by-step explanation:
To find the margin of error at a 95% confidence level when n = 490 and P Hat = 0.43, we need to use the formula for the margin of error (ME) of a proportion, which is:
ME = Z * sqrt((p' * (1 - p')) / n)
Firstly, we need to find the appropriate Z-value for the 95% confidence level. We can use the Z-table, calculator functions, or statistical software to determine that the Z-value at a 95% confidence level (which leaves 2.5% in each tail) is typically 1.96.
Now, we plug in the values into the formula:
ME = 1.96 * sqrt((0.43 * (1 - 0.43)) / 490)
ME = 1.96 * sqrt((0.43 * 0.57) / 490)
ME = 1.96 * sqrt(0.2451 / 490)
ME = 1.96 * sqrt(0.0005)
ME = 1.96 * 0.02236
ME = 0.043824
Rounded to three decimal places, the margin of error is 0.044.