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

question 3

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.
Can we conclude at the 10% significance level that the official was correct?

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Definitions:

Seminal Vesicle

The seminal vesicles are a pair of glands in males that secrete a significant portion of the fluid that becomes semen, providing nutrients for sperm and enhancing their motility.

Uterus

A female reproductive organ where the development of the fetus takes place during pregnancy.

Yolk Sac

An extra-embryonic membrane that provides nutrients to the early embryo; it is a critical structure in the development of many vertebrates.

Chorion

The outermost fetal membrane in many vertebrates, including humans, contributing to the formation of the placenta.