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 X-bar = 11.3 gallons, S = 3.1 gallons. • Eleven motorists purchased premium-grade gasoline. a. At the 0.10 level of significance, is there evidence that the population mean purchase was different from 10 gallons? Interpret your decision. b. Determine the p-value in (a) and show your calculations step by step. Interpret the meaning of the p-value. c. At the 0.10 level of significance, is there evidence that less than 20% of all the motorists at the station purchased premium-grade gasoline? Interpret your decision.
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 X-bar = 11.3 gallons, S = 3.1 gallons.
• Eleven motorists purchased premium-grade gasoline.
a. At the 0.10 level of significance, is there evidence that the population mean purchase was different from 10 gallons? Interpret your decision.
b. Determine the p-value in (a) and show your calculations step by step. Interpret the meaning of the p-value.
c. At the 0.10 level of significance, is there evidence that less than 20% of all the motorists at the station purchased premium-grade gasoline? Interpret your decision.
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?
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