A survey of residents in a particular town indicated that 30% of the residents favour building a community centre and the others opposed it. Ten residents are randomly surveyed and asked if they favour the proposed new community centre.

Question

Determine the standard deviation.

Answer 1

First, we need to calculate the standard deviation of the population proportion who favor building a community center.

Given:
- Sample size (n) = 10
- Population proportion favoring the community center (p) = 0.30
- Population proportion opposing the community center (q) = 1 - p = 0.70

Standard deviation of population proportion:
σ = sqrt[(p*q) / n]
σ = sqrt[(0.30 * 0.70) / 10]
σ = sqrt[0.21 / 10]
σ = sqrt(0.021)
σ = 0.145

Therefore, the standard deviation is approximately 0.145.