A city planner would like to estimate the true mean annual income of all households in the city. She selects a random sample of 50 households and determines that the 99% confidence interval for the true mean annual income of all households in the city to be $42,000 to $68,000. If the city planner had selected 100 households rather than 50 households, what effect would this have had on the margin of error of the interval? It would have doubled.
It would have been cut in half.
It would have remained the same.
It would have been smaller, but it would not have been cut in half.