SOLUTION: 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

Question 1189640: 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 2 6 4 1
Assume that the amount of gas remaining in tanks is normally distributed with a standard deviation of 1 gallon.
Can we conclude at the 10% significance level that the official was correct?
a. State the null and alternative hypotheses.
b. Compute the value of the test statistic.
c. Compute the p-value.

d. Interpret the results.
e. Estimate with 90% confidence interval the mean of gas remaining in tanks

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
sd of sample is 1.475 gallons, mean is 3.2 gallons.
Ho: mean amount was >=3 gallons
Ha: mean amount was <3 gallons
alpha=0.10 p{reject Ho|Ho true}
test is a t (0.90, df=9)
critical value is t > +1.833
t=(3.2-3)/1.475/sqrt(10)
=0.43. This is < critical value
fail to reject Ho; the amount of gas in the tanks could be < 3 gallons
p-value=0.34, as expected with fail to reject, p-value is > alpha.
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90%CI half-interval is t*s/sqrt(n)= 1.833*1.475/sqrt(10)=0.85
interval is (2.35, 4.05) gallons

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