A town\'s department of public works is concerned about adverse public reaction

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. Number 1 2 3 4 5 6 7 8 Opposed 10 8 12 6 4 14 8 10 Please keep 4 decimals. (1) p-bar = ? (2) Calculate the UCL and LCL. (3) Is the community sentiment stable?

Explanation / Answer

1) P-bar = total opposed/ total sample observation

= 72/8*100

=0.09

2) Consider 3-sigma limits

UCL = P-bar + z* sqrt(pbar(1-pbar)/n)

=0.09 + 3*sqrt(0.09*(1-.09)/100)

= 0.18

LCL = P-bar - z* sqrt(pbar(1-pbar)/n)

= 0.09 - 3*sqrt(0.09*(1-.09)/100)

= 0.004

3) Few proprtion opposed (0.1,.12,.14) are above the UCL (0.09) .this shows that community sentiments are not stable i.e is within UCL and LCL

Sample Opposed Proportion opposed 1 10 0.1 2 8 0.08 3 12 0.12 4 6 0.06 5 4 0.04 6 14 0.14 7 8 0.08 8 10 0.1 Total 72

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