Question

Over the past 20 years, annual rainfall in Las Vegas averaged 485.755 mm with a standard deviation of 90.34 mm. a. Formulate a 95% two-sided confidence interval on the average annual rainfall in Las Vegas. b. Compute a 95% two-sided prediction interval for next year’s rainfall

Answer 1

Here annual rainfall of last 20 years = = 485.755 mm

standard deviation = s = 90.34mm

standard error of avergae rainfall in las vegas = se₀ = 90.34/sqrt(20) = 20.200mm

(a) 95% two-sided confidence interval on the average annual rainfall in Las Vegas

= +- Z_95% * se₀

= 485.755 +- 1.96 * 20.200

= (446.16 mm , 525.35 mm)

(b) 95%  two-sided prediction interval for next year’s rainfall

= +-  Z_95% * s * sqrt(1 + 1/n)

= 485.755 +- 1.96 * 90.34 * sqrt(1 + 1/20)

= 485.755 +- 1.96 * 90.34 * 1.0247

= (304.315, 667.195)