Question

Researchers want to survey the mass of American alligators in a certain region. They want to maximize the efficiency of this effort and get as many measurements as possible. Capturing alligators, putting them on a scale, and releasing them involves risk and time and subjects the animals to stress. They decide to survey alligators from the air. In this manner, they can measure the length of the animals. They want to use these measurements to estimate the mass of the alligators. They have access to data about the length and mass of captive alligators that they want to use to predict the mass of wild alligators. Which of the following best describes the alternate hypothesis for a t-test on the slope of the line relating alligator length and weight?
a. The slope of the line describing the relationship between length and mass is not equal to zero.
b. The mass of alligators increases as a function of length.
c. The slope of the line between length and mass is zero.
d. The mass of alligators decreases as a function of the length.

Answer 1

Answer:

The correct option is (a) Hₐ: β ≠ 0.

Step-by-step explanation:

In this case the researchers want to survey the mass of American alligators in a certain region.

The mass of the American alligators are considered as the dependent variables and the researchers wants to predict the mass of wild alligators from the data collected for the length of the alligators.

That is, they want to test the relationship between the mass and length of the alligators.

A t-test for the significant slope coefficient can be used to perform the test.

The hypothesis to test this can be defined as follows:

H₀: The slope of the line describing the relationship between length and mass is 0, i.e. β = 0.

Hₐ: The slope of the line describing the relationship between length and mass is not 0, i.e. β ≠ 0.

Thus, the alternate hypothesis for a t-test on the slope of the line relating alligator length and weight is, Hₐ: β ≠ 0.

The correct option is (a).