Question 10.7: Suppose a new motor fuel has been tested on 30 similar cars,......

A Guide to Business Mathematics [1175877]

Suppose a new motor fuel has been tested on 30 similar cars, and the fuel consumption was 44.1 mpg with a standard deviation of 2.9 mpg. Calculate a 95% confidence interval for the fuel consumption of this model of car.

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The sample mean is 44.1, the sample standard deviation is 2.9, the sample size is 30 and the confidence factor is 1.96; so the 95% confidence interval is

\bar{x}\,\pm\,z\frac{s}{\sqrt{n}}=44.1\,\pm\,1.96\mathrm{~*~}\frac{2.9}{\sqrt{30}}

= 44.1 ± 1.96 * 0.5295

= 44.1 ± 1.0378

= (43.0622, 45.1378)

That is, we can say with 95% confidence that the fuel consumption for this model of car is between 43.0 and 45.1 mpg.

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