Problem 7 The owner of a gasoline station wants to study gasoline purchasing hab
ID: 3179086 • Letter: P
Question
Problem 7 The owner of a gasoline station wants to study gasoline purchasing habits of motorists
at his station. He selects a random sample of of 60 motorists during a certain week, with the
following results: The amount purchased was x = 11.3 gallons, s=3.1 gallons. Ten motorists
purchased premium-grade gasoline. = 0.05.
c. Is there evidence that the population mean purchase was different than 10 gallons?
d. Is there evidence that the percentage of all the motorists at the station who purchased premium-
grade gasoline is less than 20%? What is the p-value?
e. Is there evidence that the percentage of all the motorists at the station who purchased premium-
grade gasoline is different than 20%? What is the p-value?
f. Is there evidence that the percentage of all the motorists at the station who purchased premium-
grade gasoline is more than 20%? What is the p-value?
Explanation / Answer
(C)
Below are the null and alternate hypothesis
H0: mu = 10
H1: mu not equals to 10
sample mean =11.3, sample std. dev. = 3.1 and sample size = 60
value of test statistics,
t = (11.3 - 10)/(3.1/sqrt(60)) = 3.2483
degrees of freedom = 60 - 1 = 59
p-value for t=3.25 and df = 59
p-value = 0.001908
As p-value is less than significance level, we reject the null hypothesis.
This means there is significant evidence that the mean purchase is different than 10 gallons.