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.
Determine the standard deviation.
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.