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Calculus/Confidence interval

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Expert: - 2/1/2010


Question
A car leasing firm is interested in the average usage of fuel (in litres) per 100 km for a certain car model.
A random sample of 8 cars is taken.

Car (#)..... Fuel used per 100 km (litres)
1............7.4
2............6.6
3............7.7
4............8.3
5............6.5
6............6.9
7............7.8
8............6.4

Calculate a 99% confidence interval for the standard deviation in fuel used per 100 km?

Answer
The formula for the standard deviation is (sum(xi˛) - [sum(xi)]˛/n)/(n-1).

In this case, n=8, so n-1 = 7.

The sum is 57.6, so the sum˛ is 3,317.76.  If that is taken over n (8), we get 414.72.

The sum of squares is 418.16.

The difference is 3.44.

If that is divided by 7, the answer is roughly 0.49.

This is the variance.  The standard deviation is the squareroot, which is 0.7.

The two sided standard normal is at 99% is at 2.575 standard deviations.

This makes the amount of variance ±1.8.

To find the average, take the sum of 57.6 and divide by 8.  This should give 7.2.

So the answer should be 7.2 ± 1.8.

Calculus

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