2. An educational testing service designed an achievement test so that the range in student scores would be greater than 300 points. To determine whether the objective was achieved, the testing service gave the test to a random sample of 31 students and found that the sample mean and variance were 761 and 2277, respectively. Specify the null and alternative hypotheses for determining whether the test achieved the desired dispersion in scores. Assume that range = 6. Formulate appropriate hypothesis and test the hypothesis at 0.05 level based on the rejection region