Question

In a poll of 400 voters in a certain state61% said they opposed a voter ID bill that might hinder some legitimate votersfrom voting. The margin of error in the poll was reported at 4 percentage points ( with a 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 sampl size is too small to acheive the stated margin of error.

D. For the given sample size, the margin of error should be smaller than stated.

Answer 1

The margin of error for the test for proportion is computed as:

p = 0.61 and n = 400 here. Putting these values and the MOE = 0.04 as the computed margin of error, we get here:

Now for 95% confidence interval, we know from the standard normal tables that:

P( -1.65 < Z < 1.65 ) = 0.95

Therefore, 1.65 is the critical z value that is used for the margin of error here which is very close to the computed 1.64 value as the critical z value.

Therefore the reported margin of error is consistent with the sample size here.