Question

6.4.5 A study of 29 female Sumatran elephants provided a 95% confidence interval for the mean shoulder height as (197.2, 235.1) cm.24 Consider a new study to estimate the mean shoulder height of male Sumatran elephants.

Answer 1

6.4.5 Margin of error for females = (upper bound - lower bound)/2 = (235.1-197.2)/2 = 18.95

Significance level, α = 1-0.95 = 0.05

Critical value at 0.05, z = NORM.S.INV(0.05/2) = 1.96

E = z*(σ/√n)

so, σ = (E*√n) / z = (18.95*√29 ) / 1.96 = 52.0658

Sample size for male:

Standard deviation for males = Standard deviation for females = 52.0658

Margin of error for males = 10

Sample size, n = (z * σ / E)² = (1.96 * 52.0658 / 10)² = 104.14 = 104