Question

A town's department of public works is concerned about adverse public reaction to a sewer project that is currently in progress. Because of this, the Commissioner of Public Works has authorized a weekly survey to be conducted of town residents. Each week, a sample of 100 residents is questioned on their feelings towards the project. The results to date are shown below. Analyze this data using a P-chart with a 5% risk of Type I error (Z=3). Is the community sentiment stable?
                       
Week        1    2    3 4 5 6 7 8

Opposed 10 8 12 6 4 14 8 10

a) Determine the upper control limit (UCL) of P-chart.
b) Determine the lower control limit (UCL) of P-chart.
c) Is the community sentiment stable?

Answer 1

Ans.

Week	Sample space	Opposed(np')
1	100	10
2	100	8
3	100	12
4	100	6
5	100	4
6	100	14
7	100	8
8	100	10
	Total= 800	total = 72

The next step is to calculate the average fraction defective. To determine the average, we add up all the np values and divide by the sum of all the n values. The sum of the np values is 72; the sum of the n values is 800. The average is then calculated as:

= 72 / 800 => 0.09 = 9%

= 800/8 => 100

The next step is to determine the average subgroup size. Since the subgroup size is constant, the average subgroup size is 100. This average calculation is shown in the second equation where k is the number of subgroups. The next step is to calculate the control limits. The control limits calculations are shown below :

= 0.09 + 3 x 0.0286 => 0.1758

Therefore corrected with error 5% UCLp' = 0.1758 + 3( 5%) = 0.33

Ans(b)

Similarly ,

LCLp'  = 0.09 - 3 x 0.0286 => 0.1758

Therefore corrected with error 5% LCLp' = 0.1758 - 3( 5%) = 0.146

Ans(c) Sentiment appears to be stable, in that none of the eight weeks is outside these limits.