The report referenced in the previous exercise also indicated that 33% of those in a representative sample of 533 homeowners in southern states said that they had considered installing solar panels. 

a. Use the given information to construct and interpret a 90% confidence interval for the proportion of all homeowners in the southern states who have considered installing solar panels.

b. Give two reasons why the confidence interval in Part (a) is narrower than the confidence interval calculated in the previous exercise.