Question

In 25 test runs the gasoline consumption of an experimental engine had a mean 6.3 gallons and a standard deviation of 1.8 gallons. Construct a 95% confidence interval for the σ, which measures the true variability of the gasoline consumption of the engine.

Answer 1

df = n - 1 = 25 - 1 = 24

chi-square critical values at 0.05 significance level with 24 df = 12.401 , 39.364

95% confidence interval for is

Sqrt [ ( n - 1) S2 / U ] < < Sqrt [ ( n - 1) S2 / L ]

sqrt [ 24 * 1.82 / 39.364 ] < < sqrt [ 24 * 1.82 / 12.401 ]

1.41 < < 2.50

95% CI for is ( 1.41 , 2.50 )