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:

0.17
0.18
0.08
0.15
0.15
0.07
0.07

Assuming that this sample is representative of the cars in​ use, construct a 98​% confidence interval estimate of the mean amount of​ nitrogen-oxide emissions for all cars.

_ g/mi <μ< _ g/mi

Answer 1

	Values ( X )	Σ ( Xi- X̅ )2
	0.17	0.0021
	0.18	0.0031
	0.08	0.002
	0.15	0.0007
	0.15	0.0007
	0.07	0.0029
	0.07	0.0029
Total	0.87	0.0144

Mean X̅ = Σ Xi / n
X̅ = 0.87 / 7 = 0.1243
Sample Standard deviation S_X = √ ( (Xi - X̅ )2 / n - 1 )
S_X = √ ( 0.0144 / 7 -1 ) = 0.049

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.02 /2, 7- 1 ) = 3.143
0.1243 ± t(0.02/2, 7 -1) * 0.049/√(7)
Lower Limit = 0.1243 - t(0.02/2, 7 -1) 0.049/√(7)
Lower Limit = 0.0661
Upper Limit = 0.1243 + t(0.02/2, 7 -1) 0.049/√(7)
Upper Limit = 0.1825
98% Confidence interval is ( 0.0661 , 0.1825 )