Describe how the shape, center, and spread of t -models change as the number of degrees of freedom increases. Choose the correct answer below. A. Shape becomes farther from Normal, center does not change, spread becomes narrower. B. Shape becomes closer to Normal, center does not change, spread becomes wider. C. Shape becomes farther from Normal, center does not change, spread becomes wider. D. Shape becomes closer to Normal, center does not change, spread becomes narrower.

Question

Mathematics

Ingrid Jackson

18 November, 19:31

Describe how the shape, center, and spread of t -models change as the number of degrees of freedom increases. Choose the correct answer below. A. Shape becomes farther from Normal, center does not change, spread becomes narrower. B. Shape becomes closer to Normal, center does not change, spread becomes wider. C. Shape becomes farther from Normal, center does not change, spread becomes wider. D. Shape becomes closer to Normal, center does not change, spread becomes narrower.

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Answers (1)

Know the Answer?

Abril Mckenzie · Answer 1

For this question we know that the t distribution present the same parameter for the mean like the normal distribution 0, so then we can conclude that the center does not change.

When the degrees of freedom of the t distribution increases we have a bettwer approximation to the normal distribution.

And when the degrees of freedom increase we have that the measure of variation for the t distribution is reduced and we can conclude that when the degrees of freedom increases we have a ditribution more narrower.

So then the best answer for this case would be:

D. Shape becomes closer to Normal, center does not change, spread becomes narrower.

Step-by-step explanation:

Previous concepts

The t distribution (Student's t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".

The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.

The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."

Solution to the problem

For this question we know that the t distribution present the same parameter for the mean like the normal distribution 0, so then we can conclude that the center does not change.

When the degrees of freedom of the t distribution increases we have a bettwer approximation to the normal distribution.

And when the degrees of freedom increase we have that the measure of variation for the t distribution is reduced and we can conclude that when the degrees of freedom increases we have a ditribution more narrower.

So then the best answer for this case would be:

D. Shape becomes closer to Normal, center does not change, spread becomes narrower.