An Educational Testing Service Designed an Achievement Test So That $H _ { 0 } : \sigma ^ { 2 } = 4900$

Essay

An educational testing service designed an achievement test so that the range in student scores would be greater than 420 points. To determine whether the objective was achieved, the testing service gave the test to a random sample of 30 students and found that the sample mean and variance were 759 and 1943, respectively. Conduct the test for $H _ { 0 } : \sigma ^ { 2 } = 4900$ vs. $H _ { \mathrm { a } } : \sigma ^ { 2 } > 4900$ using $\alpha = .025$ . Assume the range is $6 \sigma$ .