Question

During the last energy crisis, a government official claimed that the average car owner refilled the tank when there was more than 3 gallons left. To check the claim, 10 cars were surveyed as they entered a gas station. The amount of gas was measured and recorded as shown below

            3          5         3         2         3         3         7         6         4         4

Assume that the amount of gas remaining in tanks is normally distributed with a standard deviation of 1 gallon.

Can we conclude at the 5% significance level that the official was correct?

Answer 1

X :  The amount of gas was measured

	X	X-X̅	(X-X̅)2
	3	-0.7	0.49
	5	1.3	1.69
	3	-0.7	0.49
	2	-1.7	2.89
	3	-0.7	0.49
	7	3.3	10.89
	6	2.3	5.29
	4	0.3	0.09
	4	0.3	0.09
Total	37		22.41
mean=X̅	Total/10
X̅=	3.7