The National Sample Survey identifies a segment of Indian households as the “Mature Middle Class” with an income of around 170,000 rupees per year. The rapid growth of the Indian economy has resulted in an increase in the proportion of households in this group, and the survey estimates that it increased from 27% in 2005 to 50% in 2011. What sample size is necessary in order to conclude that the proportion of the Indian population in this group increased between 2005 and 2011 at the 99% significance level? You can assume that the size of the sample is the same in 2005 and in 2011.