In an effort to reduce energy costs, a major university has installed more effic

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 significantly reducts costs, the university takes a sample of 111 classrooms. THey find that the average cost for 1 week is $244 with a standard deviation of $79. When testing the hypothesis (at the 1% level of significance) that the average energy use has decreased from the past, what is the critical value? (Please round your answer to 2 decimal places).

Explanation / Answer

SOLUTION:

Here in the problem, we see that they are give that ,sample(n)=111,Population mean=265, sample mean=$244/week and sample standard deviation=$79/ week. But when we testing the hypothesis at 1% level of significance we observe that the population standard deviation is NOT known, so here for finding the critical value we use t-test .

To find t-test critical:

Degrees of freedom = n-1 = 111-1 = 110.
The t-critical value for a left-tailed test, for 1% level of significance with df=110 is:
  
--> tc = 2.361

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