The tDistribution
The tdistribution is a relative of the normal distribution. It has a bell shape with values more spread out around the middle. That is, it’s not as sharply curved as the normal distribution, which reflects its ability to work with problems that may not be exactly normal but are close.
Solve the following problems about the tdistribution, its traits, and how it compares to the Zdistribution.
Sample questions

Which of the following is true of the tdistribution, as compared to the Zdistribution? (Assume a low number of degrees of freedom.)
(A) The tdistribution has thicker tails than the Zdistribution.
(B) The tdistribution has a proportionately larger standard deviation than the Zdistribution.
(C) The tdistribution is bellshaped but has a lower peak than the Zdistribution.
(D) Choices (A) and (C)
(E) Choices (A), (B), and (C)
Answer: E. Choices (A), (B), and (C) (The tdistribution has thicker tails than the Zdistribution; the tdistribution has a proportionately larger standard deviation than the Zdistribution; the tdistribution is bellshaped but has a lower peak than the Zdistribution.)
Compared to the Zdistribution, the tdistribution has thicker tails and a proportionately larger standard deviation. It’s still bellshaped, but it has a lower peak than the Zdistribution.

Which tdistribution do you use for a study involving one population with a sample size of 30?
Answer: t_{29}
A tdistribution for a study with one population with a sample size of 30 has n – 1 = 30 – 1 = 29 degrees of freedom, so the correct distribution is t_{29}.

If you graphed a standard normal distribution (Zdistribution) on the same number line as a tdistribution with 15 degrees of freedom, how would you expect them to differ?
Answer: The peak of the Zdistribution would be higher, and the tdistribution would have thicker tails.
In general, the tdistribution is bellshaped but is flatter and has a lower peak than the standard normal (Z) distribution, particularly with smaller degrees of freedom for the tdistribution.

Given different tdistributions with the following degrees of freedom, which one would you expect to most closely resemble the Zdistribution: 5, 10, 20, 30, or 100?
Answer: 100
As the degrees of freedom increase, the tdistribution tends to look more like the Zdistribution. So the tdistribution with the highest degrees of freedom most resembles the Zdistribution.
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