Question

6. The owner of a gas station wants to study gasoline purchasing habits of motorists at this station. He selects a random sample of 60 motorists during a certain week, with the following results: The amount of gas purchased was; mean = 11.3 gallons, standard deviation = 3.1 gallons; Eleven motorists purchased premium-grade gasoline (4 points)

1. At the 0.05 significance level, is there evidence that the population mean purchase was different from 10 gallons? (1 point)

2. Determine the p-value in part (a) (1 point)

3. At the 0.05 significance level, is there evidence that less than 20% of all the motorists at the station purchased premium-grade gasoline? (1 point)

4. What is your answer to part (a) if the sample mean equals 10.3 gallons? (1 point)

Answer 1

part a)

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = 3.2483

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 3.2483 ) = 0.0019
Reject null hypothesis if P value < level of significance
P - value = 0.0019 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficient  evidence to support the claim that the population mean purchase was different from 10 gallons.

Part b)

P - value = P ( t > 3.2483 ) = 0.0019

Part c)

To Test :-

H0 := P = 0.2

H1 :- P < 0.2

n = 60

Test Statistic :-


Z = -0.32

Test Criteria :-
Reject null hypothesis if

= -0.32 > -1.645, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( Z < -0.32 )
P value = 0.3745
Reject null hypothesis if P value <
Since P value = 0.3745 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence to support the claim that  less than 20% of all the motorists at the station purchased premium-grade gasoline.

Part d)

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = 0.7496

Test Criteria :-
Reject null hypothesis if


Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 0.7496 ) = 0.4565
Reject null hypothesis if P value < level of significance
P - value = 0.4565 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is insufficient  evidence to support the claim that the population mean purchase was different from 10 gallons.