THE OWNER OF A GASOLINE STATION WANTS TO STUDY GASOLINE PURCHASING HABITS OF MOTORISTS AT HIS STATION. HE SELECTS A RANDOM SAMPLE OF 60 MOTORISTS DURING A CERTAIN WEEK, WITH THE FOLLOWING RESULTS: THE AMOUNT PURCHASED WAS A SAMPLE MEAN = 11.3 GALLONS; S = 3.1 GALLONS. ELEVEN MOTORISTS PURCHASED PREMIUM-GRADE GASOLINE.
FIND: AT THE 0.05 LEVEL OF SIGNIFICANCE , IS THERE EVIDENCE THAT THE POPULATION MEAN PURCHASED WAS DIFFERENT FROM 10 GALLONS ?
H0: = 10
Ha: 10
Test statistics
t = - / S / sqrt(n)
= 11.3 - 10 / 3.1 / sqrt( 11)
= 1.39
This is test statistics value.
critical value at 0.05 level with 10 df = -2.228 , 2.228
Since test statistics falls in non-rejection region , we do not have sufficient evidence to reject H0.
We conclude at 0.05 level that we fail to support the claim.
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