A study reports that 5% of all US households make a weather-related insurance claim on their house. In a random sample of 500 Raleigh households, 30 households report that they had experienced a weather-related claim. Construct a 95% confidence interval for the true proportion of Raleigh households that have experienced a weather-related claim. Assume conditions have been met.

1. A second random sample of households was taken that was half the size of the original sample. In the second sample, 6% of households had filed a weather-related insurance claim. Determine the value of the margin of error based on the second sample of households that would be used to compute an interval for p with the same confidence level as that of the original interval.