A social scientist plans a study of adult South Africans living in townships on the outskirts of Cape Town, to investigate educational attainment in the black community. Many of the study’s potential subjects were forced to leave Cape Town in 1966 when the government passed a law forbidding blacks to live in the inner cities.

Under the apartheid system, black South African children were not required to attend school, so some residents had very little education. How large a sample size is needed so that a 95% confidence interval for the mean number of years of education completed has margin of error equal to 1 year? There is no information about the standard deviation of educational attainment, but researchers expect that nearly all values fall between 0 and 18 years.