The owner of a gasoline station wants to study gasoline purchasing habits of mot

Question

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.

a. Is there evidence that the population mean purchase was greater than 10 gallons?

b. Is there evidence that the population mean purchase was less than 10 gallons?

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

a)

Here we have
n = 60, x bar = 11.3 ,
S = 3.1

The hypotheses are:

H0 : mu < =10

Ha : mu > 10

Test statistic:

t = ( x bar - mu ) / ( s / sqrt(n))

t = ( 11.3 - 10 ) / ( 3.1 / sqrt(60))

t = 3.24

Now, we need to find p value by t = 3.24 and df = 60 -1 = 59

p value = .000983.

Here, p valie is less than 0.05 , so, we reject the null hypothesis.

There is sufficient evidence that the population mean purchase was greater than 10 gallons

b)

a)

Here we have
n = 60, x bar = 11.3 ,
S = 3.1

The hypotheses are:

H0 : mu > =10

Ha : mu < 10

Test statistic:

t = ( x bar - mu ) / ( s / sqrt(n))

t = ( 11.3 - 10 ) / ( 3.1 / sqrt(60))

t = 3.24

Now, we need to find p value by t = 3.24 and df = 60 -1 = 59

p value = .000983.

Here, p valie is less than 0.05 , so, we reject the null hypothesis.

There is sufficient evidence that the population mean purchase was less than 10 gallons

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