Basic Statistics20815 marksNumerical: confidence interval proportionConfidence interval for population proportion
A sample survey of 80 customers shows that 56 are satisfied with an IT service. Estimate the proportion of satisfied customers in the population with a 95% confidence interval. n = 80, quad x = 56
A sample survey of 80 customers shows that 56 are satisfied with an IT service. Estimate the proportion of satisfied customers in the population with a 95% confidence interval. $n = 80, \quad x = 56$ [5]
- Sample size: $n = 80$ - Number satisfied: $x = 56$ - Confidence level: $95%$, so $z{\alpha/2} = 1.96$ $$\hat{p} = \frac{x}{n} = \frac{56}{80} = 0.70$$ $$SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} = \sqrt{\frac{0.70 \times 0.30}{80}} = \sqrt{\frac{0.21}{80}}$$ $$SE = \sqrt{0.0026250} = 0.05123$$ ...