Question

The growing seasons for a random sample of 34 US cities were recorded, yielding a sample mean of 188.1 days And the population standard deviation of 53.1 days. Estimate the true population mean of the growing season with 95% confidence

Answer 1

(170.251 ; 205.949)

Explanation:

Sample size, n = 34

Sample mean, xbar = 188.1

Population standard deviation, σ = 53.1

Confidence level = 95% ; Zcritical at 95% = 1.96

Using the confidence interval relation :

Xbar ± standard Error

Standard Error = Zcritical * σ/√n

Standard Error = 1.96 * 53.1/√34

Standard Error = 17.849

Lower boundary = (188.1 - 17.849) = 170.251

Upper boundary = (188.1 + 17.849) = 205.949

(170.251 ; 205.949)