Question

(15.34) The level of nitrogen oxides (NOX) in the exhaust of cars of a particular model varies Normally with mean 0.21 g/mi and standard deviation 0.05 g/mi. A company has 20 cars of this model in its fleet. What is the level L (±0.0001) such that the probability that the average NOX level x¯¯¯ for the fleet is greater than L is only 0.03? L =

Answer 1

a level of significance of 0.01 = 1%

Explanation:

given

Z = 0.0001

mean μ=0.21 g/mi

variate x= 0.21 + 0.03

standard deviation σ= 0.05 g/mi.

N = sample population 20 cars

z = (x −μ )/[σ /√N ]

Z =
`(x −μ)/((σ)/(√N) )`

Z = 0.03/ (0.05/√20) = 0.03/0.0111

Z = 2.63 +- 0.0001

Z= 2.6301 or 2.6299

checking the level of significance table from a statistical book gives

a level of significance of 0.01 = 1%

therefore the null hypothesis is accepted.