##### Question

# A consulting firm advises its clients about sampling and statistical procedures that can be used…

A consulting firm advises its clients about sampling and statistical procedures that can

be used to control their manufacturing processes. In one particular application, a client

gave them a sample of 800 observations taken during a time in which that client’s

process was operating satisfactorily. The sample standard deviation for these data was

0.21; hence, with so much data, the population standard deviation was assumed to be

0.21. The consulting firm then suggests that random samples of size 30 be taken

periodically to monitor the process on an ongoing basis. By analyzing the new sample,

the client could quickly learn whether the process was operating satisfactorily. When

the process was not operating satisfactorily, corrective action could be taken to

eliminate the problem. The design specification indicated the mean for the process

should be 12. Corrective action will be taken any time the mean is not 12. The following

sample was collected at hourly intervals during the first day of operation of the new

statistical control procedure.

11.55 11.62 11.52 11.75 11.90 11.64 11.80 12.03 11.94 11.92

12.13 12.09 11.93 12.21 12.32 11.93 11.85 11.76 12.16 11.77

12.00 12.04 11.98 12.30 12.18 11.97 12.17 11.85 12.30 12.15

1. Describe five characteristic of normal distribution.

(1 marks)

2. What is Type I and Type II error in this case?

(1 marks)

3. Conduct a hypothesis test to determine whether any correction action should be

taken at 5% significance level if the analysis is based on

a. The first 10 data in the sample only

b. The first 20 data in the sample only

c. All data in the sample

(6 marks)

4. Based on the result in question 3, discuss the implications of changing the

sample size to a larger value for this case. Support your answer with numerical

values.

(2 marks)

(Total 10 marks