Question

Inter State Moving and Storage Company is setting up a control chart to monitor the proportion of residential moves that result in written complaints due to late delivery, lost Items, or damaged items. A sample of 60 moves is selected for each of the last 12 months. The number of written complaints in each sample is 8, 7, 2, 3, 4, 5, 12, 7, 9, 6, 6, and 14. points Click here for the Excel Data File a. Insert the mean proportion defective, UCL, and LCL. (Round your Intermediate calculations and final answers to 2 decimal places.) Answer is not complete. Mean proportion defective UCL LCL c. Does It appear that the number of complaints is out of control for any of the months? No Yes

Answer 1

Answer to 1st Question:
The following table shows the calculations -

Month	Number of Defectives in each sample	Proportion defective(pi)
1	8	0.1333
2	7	0.1167
3	2	0.0333
4	8	0.1333
5	4	0.0667
6	5	0.0833
7	12	0.2
8	7	0.1167
9	9	0.15
10	6	0.1
11	6	0.1
12	14	0.2333
Total		1.4666

Mean proportion defective, $\bar{p}$ = 1.4666 / 12 = 0.12(approximately)

Number of observations, n = 12

The formula for control limits -

U.C.L. = $\bar{p}$ + A ($\bar{p}$ (1 - $\bar{p}$ ) )0.5 (where, A = 3 / n0.5)

L.C.L. = $\bar{p}$ - A ($\bar{p}$ (1 - $\bar{p}$ ) )0.5 (where, A = 3 / n0.5)

Substituting the values,

U.C.L. = 0.41

L.C.L. = -0.1614

Since, L.C.L. is negative it would be taken as 0

Therefore,

Mean Proportion Defective	0.12
U.C.L.	0.41
L.C.L.	0

Answer to 2nd Question:
Since all the observations lie inside the control limits, the number of complaints are not out-of-control

Hence, NO is the correct option