An Educational Testing Service Designed an Achievement Test So That $$= 6 \sigma$$

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 52 students and found
that the sample mean and variance were 733 and 2255, respectively. Specify the null and
alternative hypotheses for determining whether the test achieved the desired dispersion in
scores. Assume that range $$= 6 \sigma$$