Question: Physical Sciences The design specifications for a new gymnasium at a local high school call for the lights to produce at least 40 footcandles (a measure of brightness). Before the new facility was opened to students, the contractor collected a sample of 23 brightness measurements at random locations in the gym. The sample mean was x = 38.63 footcandles and the sample standard deviation was s = 5.6 footcandles.
a. Is there any evidence to suggest the mean brightness in the gym is less than the design specification? Assume normality and use a = 0.01.
b. Find bounds on the p value associated with this hypothesis test.