In a poll of 400 voters in a certain state, 61% said that they opposed a voter ID bill that might hinder some legitimate voters from voting. The margin of error in the poll was reported as 4 percentage points (with a 95% degree of confidence). Which statement is correct?
A. The reported margin of error is consistent with the sample size.
B. There is not enough information to determine whether the margin of error is consistent with the sample size.
C. The sample size is too small to achieve the stated margin of error.
D. For the given sample size, the margin of error should be smaller than stated.
The sample size is too small to achieve the stated margin of error.
The answer is: The reported margin of error is consistent with the sample size.
C. The sample size is too small to achieve the stated margin of error.
To determine which statement is correct, we need to review the information provided.
The poll was conducted with a sample size of 400 voters in the state. The reported margin of error is 4 percentage points with a 95% degree of confidence.
In order to decide which statement is correct, we need to verify if the reported margin of error is consistent with the sample size. The formula for calculating the margin of error is:
Margin of Error = Critical Value x (Standard Deviation / Square Root of Sample Size)
The critical value is determined by the desired degree of confidence. For a 95% degree of confidence, the critical value is approximately 1.96.
The standard deviation is not provided in the question, but we can estimate it using the information given. The approximate standard deviation can be calculated by taking the square root of the product of the sample proportion (0.61) and the complement of the sample proportion (1 - 0.61):
Standard Deviation ≈ √[(0.61 × 0.39) / 400]
Calculating this estimation yields a standard deviation of approximately 0.024.
Now we can calculate the margin of error:
Margin of Error ≈ 1.96 × (0.024 / √400)
This calculation yields a margin of error of approximately 0.047, which is equivalent to 4.7 percentage points.
Comparing the calculated margin of error (4.7 percentage points) to the reported margin of error (4 percentage points), we can conclude that the reported margin of error is consistent with the sample size.
Therefore, the correct statement is:
A. The reported margin of error is consistent with the sample size.