D Question 2 50 pts 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. a. Consider the confidence interval I. Does the confidence interval provide convincing statistical evidence that the true proportion of Raleigh households that experience weather-related insurance claims is different from the claims made by US households? Justify your answer. II. Does the confidence interval provide convincing statistical evidence that 5% of Raleigh households make insurance claims? Justify your answer. b. 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