SOLUTION: 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
Algebra.Com
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.
RELATED QUESTIONS
Nationwide, the average waiting time until a electric utility customer service... (answered by stanbon)
Assume that in a hypothesis test with null hypothesis 0 μ H : = 13.0 at a = 0.05,... (answered by stanbon)
Jim’s Auto Insurance Company customers sometimes have to wait a long time to speak to a (answered by math_tutor2020)
A software company has 3 customer service representatives. After a week of observation a... (answered by stanbon)
The customer service department of a large company monitors the incoming phone calls to... (answered by lynnlo)
The population mean waiting time of customers of the XYZ Burger chain is 3.4 minutes with (answered by stanbon)
A customer service call center handles 5100 calls in an 8-hour day. If the average... (answered by rfer)
The waiting time until a customer is served at a fast food restaurant during lunch hours... (answered by Boreal)
Between 11 p.m. and midnight on Thursday night, Mystery Pizza gets an average of 4.2... (answered by ikleyn)