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.

Consider the confidence interval

1. 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.
2. Does the confidence interval provide convincing statistical evidence that 5% of Raleigh households make insurance claims? Justify your answer.