A Boat Manufacturer Claims That a Particular Boat Model and Motor

question 13

Essay

A boat manufacturer claims that a particular boat model and motor combination willburn less than 4.0 gallons of fuel per hour. Fuel consumption for a random sample of10 similar boats was measured, resulting in the data below:
A consumer group is interested in determining if there is convincing evidence that themanufacturer's claim is correct.
a) What null and alternative hypotheses should the investigators use?
In a fewsentences, justify your choice of the alternative hypothesis.
b) Using a graphic technique of your choice, show that the t-procedures areappropriate to use with these data.
c) Using your hypotheses from part (a), carry out a hypothesis test using ?= 0.05and interpret the results.
d) In the context of this study, describe a Type I and a Type II error.

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Definitions:

Rival Good

A type of good where one person's consumption of the good reduces the ability of another person to consume the same good.

Exclusive Good

A product or service that is available only to certain people or groups, often due to high price or scarcity.

Public Good

A good or service offered to every member of a society for free, either by public authorities or by a private organization or person, without seeking profit.

Optimal Area

The most advantageous or efficient region or point for a specific activity or condition.