In: Statistics and Probability
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.