Question

In an effort to reduce energy costs, a major university has installed more efficient lights as well as automatic sensors that turn the lights off when no movement is present in a room. Historically, the cost of lighting an average classroom for 1 week has been $265. To determine whether the changes have signficantly reduced costs, the university takes a sample of 50 classrooms. They find that the average cost for 1 week is $247 with a standard deviation of $60. When testing the hypothesis (at the 5% level of significance) that the average energy use has decreased from the past, what is the test statistic? (please round your answer to 2 decimal places)

Answer 1

H₀: = 265

H₁: < 265

The test statistic t = ()/(s/)

                             = (247 - 265)/(60/)

                             = -2.12

At 0.05 significance level, the critical value is t_{0.05, 49} = -1.677

Since the test statistic value is less than the critical value(-2.12 < -1.677), so we should reject the null hypothesis.

So at 5% significance level there is sufficient evidence to conclude that the changes have significantly reduced the costs.