Question

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 ?

Answer 1

H0: $\mu$ = 10

Ha: $\mu$$\neq$ 10

Test statistics

t = $\bar{x}$ - $\mu$ / 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.