Question

In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results were obtained. 0.10 0.13 0.16 0.15 0.14 0.08 0.15 (a) Construct a 99% confidence interval for the mean nitrogen-oxide emissions of all cars. (b) If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/mi, based on the 99% confidence interval in (a),

Answer 1

The question is incomplete. Here is the complete qeustion.

In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results were obtained: 0.10 0.13 0.16 0.15 0.14 0.008 0.15

(a) Construct a 99% confidence interval for the mean nitrogen-oxide emissions of all cars.

(b) If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/mi, based on the 99% confidence interval in (a), can we safely conclude that this requirement is being met?

Answer: (a) 0.089 ≤ μ ≤ 0.171

(b) No

Explanation:

(a) To determine the confidence interval, first calculate the mean (X) and standard deviation (s) of the sample

X =
`(0.1+0.13+0.16+0.15+0.14+0.08+0.15)/(7)`

X = 0.13

s =
`\sqrt{((0.1-0.13)^(2) + (0.13 - 0.13)^(2) + ... + (0.15 - 0.13)^(2))/(7-1) }`

s = 0.029

The degrees of freedom is

N - 1 = 7 - 1 = 6

And since the confidence is of 99%:

α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005

The t-test statistics for
`t_(6,0.005)` is 3.707

(Value found in the t-distribution table)

Now, calculate Error:

E =
`t_(6,0.005)` .
`(s)/(√(N) )`

E = 3.707.
`(0.029)/(√(7) )`

E = 0.041

The interval will be:

0.13 - 0.041 ≤ μ ≤ 0.13+0.041

0.089 ≤ μ ≤ 0.171

(b) No, because according to the interval, the nitrode-oxide emissions range from 0.089 to 0.171, which is greater than required by EPA.