Question

In 12 test runs an experimental engine consumed on the average 12.9 gallons of gasoline per minute with a standard deviation of 1.6 gallons.
a) Construct a 90% confidence interval for the average gasoline consumption of the engine.
b) Construct a 95% confidence interval for the standard deviation.

Answer 1

Answer on Question #71011 – Math – Statistics and Probability

Question

In 12 test runs an experimental engine consumed on the average 12.9 gallons of gasoline per minute with a standard deviation of 1.6 gallons.

a) Construct a 90% confidence interval for the average gasoline consumption of the engine.

b) Construct a 95% confidence interval for the standard deviation.

Solution

a) $90\% CI = \left(\bar{x} - t_{0.05,11} \frac{s}{\sqrt{n}}, \bar{x} + t_{0.05,11} \frac{s}{\sqrt{n}}\right) = \left(12.9 - 1.796 \frac{1.6}{\sqrt{12}}, 12.9 + 1.796 \frac{1.6}{\sqrt{12}}\right) = (12.07, 13.73).$

b) $95\% CI = \left(s \sqrt{\frac{n-1}{\chi_{0.025}^2}}, s \sqrt{\frac{n-1}{\chi_{0.975}^2}}\right) = \left(1.6 \sqrt{\frac{12-1}{21.92}}, 1.6 \sqrt{\frac{12-1}{3.815}}\right) = (1.13, 2.717).$

Answer: a) (12.07, 13.73); b) (1.13, 2.717).

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