Basic Statistics20805 marksNumerical: confidence interval meanConfidence interval for population mean
The fuel consumption of a new model of cars is being tested. In one trial, 50 cars chosen at random were driven under the identical conditions and the distances, x km, covered on 1 liter of petrol were recorded. The results gave the following totals: Σ x = 525, Σ x² = 5625. Calculate the 99% confide
The fuel consumption of a new model of cars is being tested. In one trial, 50 cars chosen at random were driven under the identical conditions and the distances, x km, covered on 1 liter of petrol were recorded. The results gave the following totals: Σ x = 525, Σ x² = 5625. Calculate the 99% confidence interval for the mean petrol consumption, in km per liter. Interpret the result. [5]
- Sample size: $n = 50$ - $\Sigma x = 525$ - $\Sigma x^2 = 5625$ - Confidence level: 99% $$\bar{x} = \frac{\Sigma x}{n} = \frac{525}{50} = 10.5 \text{ km/liter}$$ Using the sample estimate of variance (with $n$ divisor, common at this level): $$s^2 = \frac{\Sigma x^2}{n} - \bar{x}^2 = \frac{5625}...