Because of the increased cost of housing, a national real estate board wants to compare the proportion of homeowners living in metropolitan areas with the proportion living in rural areas. The board members know that housing costs are higher in metropolitan areas, but they also know that small town and rural residents have substantially lower income levels. The board has decided to find out whether the corresponding proportions differ from one another. A random sample of 150 persons living in rural areas contains 93 homeowners, while a sample of 225 persons living in metropolitan areas has 126 homeowners. a). At 5% level of significance, is there evidence to support the board's intention? Your conclusion must be in terms of the P-Value. Show all necessary work. b). What type of error is possible and describe this error in terms of the problem? c). Estimate the difference in the proportion of homeowners living in rural and metropolitan areas using a 95% confidence interval. Show all necessary work. Using this interval estimation, is there sufficient evidence to support the board's intention? Explain Carefully. d). Carefully interpret the confidence interval estimation