A development economist is interested in whether average years of schooling of girls and boys are the same in a certain developing country. A random sample of 250 girls yields a mean of 5.1 years, and a standard deviation of 1.2 years. An independent random sample of 280 boys yields a mean of 6.3 years, and a standard deviation of 1.7 years.
Test the null hypothesis that mean years of schooling is the same in the populations of girls (X population) and boys (Y population), against the alternative hypothesis that the population means are different. Use a 5% level of significance.
What is the test statistic, correct form of the rejection region (graphically), and confidence interval (lower and upper end)?