Problem 7 The owner of a gasoline station wants to study gasoline purchasing hab

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.

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