(Solution) - The owner of a gasoline station wants to study gasoline -(2025 Original AI-Free Solution)

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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 = 11.3 gallons, S = 3.1 gallons.
? Eleven motorists purchased premium-grade gasoline.
a. At the 0.05 level of significance, is there evidence that the population mean purchase was different from 10 gallons?
b. Determine the p-value in (a).
c. At the 0.05 level of significance, is there evidence that less than 20% of all the motorists at the station purchased premium-grade gasoline?
d. What is your answer to (a) if the sample mean equals 10.3 gallons?
e. What is your answer to (c) if 7 motorists purchased premium- grade gasoline?