Question

The mean price of a gallon of regular gasoline in LA area was $4.04. A recently taken random sample of 50 gas stations in LA area had an average price of $3.99 for a gallon of gasoline. Assume that the standard deviation of the regular gasoline price is $0.15. An economist is interested in determining whether the mean price of regular gasoline is less than $4.04. Perform the hypothesis test at a (level of significance) = 0.05. Clearly state all 5 steps of solving the problem. Show the plot clearly.

Answer 1

Solution :

Given that ,

= 4.04

= 3.99

= 0.15

n = 50

(Step - 1) The null and alternative hypothesis is ,

H0 :   = 4.04

Ha : < 4.04

This is the left tailed test .

Test statistic = z

= ( - ) / / n

= ( 3.99 - 4.04 ) / 0.15 / 50

= -2.357

( 2 ) The test statistic = -2.357

P - value = P (Z < -2.357 ) = 0.0092

( 3 ) P-value = 0.0092

= 0.05

0.0092 < 0.05

P- value less than

P-value <

( 4 ) Reject the null hypothesis .

( 5 ) There is sufficient evidence to the test claim .