During the Gulf War, a Government Official Claimed That the Average

Essay

During the Gulf War, a government official claimed that the average car owner refilled the fuel tank when there was more than 3 litres of petrol left. To check the claim, 10 cars were surveyed as they entered a service station. The amount of petrol (in litres) was measured and recorded as shown below. $$\begin{array} { | r | r | r | r | r | r | r | r | r | r | } \hline 3 & 5 & 3 & 2 & 3 & 3 & 2 & 6 & 4 & 1 \\\hline\end{array}$$ Assume that the amount of petrol remaining in the tanks is normally distributed with a standard deviation of 1 litre.
a. Calculate the p-value.
b. Compute the probability of a Type II error if the true average amount of gas remaining in tanks is 3.5 litres.