Question

A local fire department is concerned about the waiting time from the moment a person telephones until they are connected with a service controller. In the past the mean waiting time has been 19 seconds with a standard deviation of 8 seconds. A new switchboard is being trialed to see if it reduces the mean waiting time. The department wishes to sample calls under the new conditions to see whether the new switchboard should replace the old one. A random sample of 60 calls found that the mean waiting time was 17.6 seconds.

a) Test to see if the waiting time has been reduced at the 4% level of significance. What can the fire department conclude about the effectiveness of the new switchboard?

b) Describe the Type I and Type II errors that are possible.

c) If the mean waiting time with the new switchboard is really 20 seconds, what error if any has been made?

Answer 1

a)
Below are the null and alternate hypothesis
H0: mu >= 19
Ha: mu < 19

Test statistic, z = (17.6 - 19)/(8/sqrt(60))
z = -1.3555

p-value = 0.0876

As p-value is greater than the significance level of 0.04, we fail to reject the null hypothesis.

There are not sufficient evidence to conclude that new switchboard reduces the mena waiting time.

b)
Type I error: This error occurs when we incorrectly reject the null hypothesis

Type II error: This error occurs when we incorrectly fail to reject the null hypothesis

c)
If mean waiting time is actually 20mins, there is possibility of type II error.
However there is no error made here.