A national study shows that in 2006 the average price of gas

A national study shows that in 2006 the average price of gasoline was $2.51 per gallon. The population standard deviation was shown to be $0.61. A 2007 random study of 81 Maryland gas stations showed the average price of gasoline per gallon to be $2.73. Is there significant evidence to suggest that the average price of a gallon of gasoline is more in Maryland in 2007? Test at the 10% significance level.

Solution

Set Up Hypothesis
Null, average price of a gallon of is equals to 2.51, H0: U=2.51
Alternate, average price of a gallon of gasoline is more in Maryland H1: U>2.51
Test Statistic
Population Mean(U)=2.51
Given That X(Mean)=2.73
Standard Deviation(S.D)=0.61
Number (n)=81
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=2.73-2.51/(0.61/Sqrt(81)
Zo =3.2459
| Zo | =3.2459
Critical Value
The Value of |Z | at LOS 0.1% is 1.28
We got |Zo| =3.2459 & | Z | =1.28
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Right Tail - Ha : ( P > 3.2459 ) = 0.0006
Hence Value of P0.1 > 0.0006, Here we Reject Ho