A recent study claims that girls and boys do not do equally well on math tests taken from the 2nd to 11th grades (Chicago Tribune, July 25, 2008). Suppose in a representative sample, 344 of 430 girls and 369 of 450 boys score at proficient or advanced levels on a standardized math test.

a. Construct a 95% confidence interval for the difference between the population proportions of girls and boys who score at proficient or advanced levels.

b. Develop the appropriate null and alternative hypotheses to test whether the proportion of girls who score at proficient or advanced levels differs from the proportion of boys.

c. At the 5% significance level, what is the conclusion to the test? Do the results support the study’s claim?