Question 1155043: Nationwide, the average waiting time until a electric utility customer service representative answers a call is 260 seconds. The Gigantic Kilowatt Energy Company randomly sampled 30 calls and found that, on average, they were answered in 227 seconds with a population standard deviation of 40 seconds. Can the company claim that they are faster than the average utility at α = 0.05?
A) Yes, because the test value - 4.52 falls in the critical region.
B) No, because the test value - 0.83 falls in the critical region.
C) Yes, because the test value - 0.15 falls in the critical region.
D) No, because the test value - 0.15 falls in the critical region.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
mu = 260 is the population mean
xbar = 227 is the sample mean
sigma = 40 is the population standard deviation
n = 30 is the sample size
Compute the z score
z = (xbar - mu)/(sigma/sqrt(n))
z = (227-260)/(40/sqrt(30))
z = -4.51871109941762
z = -4.52
The test statistic, or test value, is approximately -4.52
The critical value can be found through this table (tables such as this can be found in the back of your textbook). According to that table, the solution to P(Z < k) = 0.95 is roughly k = 1.645
In other words, P(Z < 1.645) = 0.95
We make this value negative because we are below the mean.
Therefore, the critical value is approximately -1.645
meaning that, P(Z < -1.645) = 0.05
Answer: A) Yes, because the test value -4.52 falls in the critical region. (the boundary is set at the critical value -1.645)
Diagram
The critical region is another name for the rejection region.
The null hypothesis is mu = 260, the alternative is mu < 260.
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