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# 15.3) During the last energy crisis, a government official

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15.3)
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 follows:
3, 2, 6, 4, 2, 5, 3, 1, 3, 3
If we assume that the amount of gas remaining in tanks is normally distributed with a standard deviation of one gallon, can we conclude at the 10% significance level that the official was correct? (Round your answer(s) to 2 decimal places.)
Appropriate test:
Test statistic =
Conclusion:
Interpretation:
Submitted: 6 years ago.
Category: Math Homework
Expert:  abozer replied 6 years ago.

abozer :

Hi,

abozer :

sample mean = 3.2

abozer :

population standard deviation = 1 (known)

abozer :

We are going to use z to test the official's claim,

abozer :

Null hypothesis: Ho: μ ≤ 3

abozer :

Alternative hypothesis: Ha: μ > 3

abozer :

test statistic = (3.2 - 3)/(1/sqrt(10))

abozer :

= 0.63

abozer :

Critical value: z = 1.282

abozer :

Conclusion: We cannot reject the null hypothesis.

abozer :

Interpretation: We do not have sufficient evidence to conclude that the average car owner refilled the tank when there was more than 3 gallons left.

abozer :

Let me know if you have any questions.