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 (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 set, labeled SAT_Writing, can also be found on the text website. Assume that scores are normally distributed.

a. Construct the null and the alternative hypotheses to test if females outscore males on the writing component of the test.
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 yourresults.

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Males Females 620 570 540 580 590 580 480 620 660 590 540 560 610 590 610 650