A Boat Manufacturer Claims That a Particular Boat Model and Motor

question 32

Essay

A boat manufacturer claims that a particular boat model and motor combination will
burn less than 4.0 gallons of fuel per hour. Fuel consumption for a random sample of
10 similar boats was measured, resulting in the data below: $$4.06,4.29,4.26,4.64,4.23,3.93,3.64,4.13,3.93,3.86$$ A consumer group is interested in determining if there is convincing evidence that the
manufacturer's claim is correct.
a) What null and alternative hypotheses should the investigators use? In a few
sentences, justify your choice of the alternative hypothesis.
b) Using a graphic technique of your choice, show that the t-procedures are
appropriate to use with these data. c) Using your hypotheses from part (a), carry out a hypothesis test using $\alpha = 0.05$ and interpret the results. d) In the context of this study, describe a Type I and a Type II error.

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Definitions:

Birth Rate

A statistical measure representing the number of births in a population over a specific time period, often per 1,000 people per year.

Death Rate

A measure of the number of deaths in a particular population, scaled to the size of that population, per unit of time.

Per Capita Growth Rate

A measure of the rate of growth per person in a population, often used in demographic or economic studies.

Birth Rate

The measure of population growth in a given area, calculated as the number of live births per thousand people per year.