Consider the data on call waiting time of customers in a call center (given Exercise). The call center has set a goal of waiting time not to exceed 35 seconds.
(a) Test to see (using α =0.05) if conducting capability analysis using normal distribution is appropriate.
(b) If not, consider a Box-Cox transformation and conduct capability analysis. Report appropriate capability indices and the percentage non-conformance.
(c) Consider conducting capability analysis using a Weibull distribution. Comment on the results.
(d) What are the drawbacks of conducting a capability analysis using the normal distribution in this example?
Exercise
A random sample of 50 observations on the waiting time (in seconds) of customers before speaking to a representative at a call center is as follows:
|
33.2
|
29.4
|
36.5
|
38.1
|
30.0
|
|
29.1
|
32.2
|
29.5
|
36.0
|
31.5 |
|
34.5
|
33.6
|
27.4
|
30.4
|
28.4
|
|
32.6
|
30.4
|
31.8
|
29.8
|
34.6
|
|
30.7
|
31.9
|
32.3
|
28.2
|
27.5
|
|
34.9
|
32.8
|
27.7
|
28.4
|
28.8
|
|
30.2
|
26.8
|
27.8
|
30.5
|
28.5
|
|
31.8
|
29.2
|
28.6
|
27.5
|
28.5
|
|
30.8
|
31.8
|
29.1
|
26.9
|
34.2
|
|
33.5
|
27.4
|
28.5
|
34.8
|
30.5
|
(a) Construct a histogram and comment on the process.
(b) What assumptions are necessary to test if the mean waiting time is less than 32 seconds?
(c) Make an appropriate transformation to satisfy the assumption stated in part (b) and validate it. Use α = 0.05.
(d) Test to determine if the mean waiting time is less than 32 seconds. Use α =0.05.
(e) Find a 90% confidence interval for the variance of waiting time.