Question: The SAT is required of most students applying for college admission in the United States. This standardized test has gone through many revisions over the years. In 2005, a new writing section was introduced that includes a direct writing measure in the form of an essay. People argue that female students generally do worse on math tests but better on writing tests. Therefore, the new section may help reduce the usual male lead on the overall average SAT score (The Washington Post, August 30, 2006). Consider the following scores on the writing component of the test of 8 male and 8 female students. The data can be found on the text website, labeled SAT Writing Component.
a. Construct the null and the alternative hypotheses to test if females outscore males on writing tests.
b. Compute the value of the test statistic. Do not assume that the population variances are equal.
c. Implement the test at α = 0.01 and interpret your results.