Chapter 1. The t Distributions

Correct. When we don’t know the value of σ, we estimate it with s, the sample standard deviation.

Incorrect. When we don’t know the value of σ, we estimate it with s, the sample standard deviation.

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Correct. Because we use “s” to estimate σ, \( \frac{ \overline{x}- \mu _{o} }{ \frac{s}{ \sqrt{n} } } \) does not have a standard Normal distribution. Rather it has a t distribution.

Incorrect. Because we use “s” to estimate σ, \( \frac{ \overline{x}- \mu _{o} }{ \frac{s}{ \sqrt{n} } } \) does not have a standard Normal distribution. Rather it has a t distribution.

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Correct. Every t distribution is specified by its degrees of freedom. For t = \( \frac{ \overline{x}- \mu _{o} }{ \frac{s}{ \sqrt{n} } } \), df = n – 1.

Incorrect. Every t distribution is specified by its degrees of freedom. For t = \( \frac{ \overline{x}- \mu _{o} }{ \frac{s}{ \sqrt{n} } } \), df = n – 1.

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Correct. Both have the same mean = zero.

Incorrect. Both have the same mean = zero.

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Correct. A t distribution with 3 degrees of freedom has a larger spread than the standard Normal distribution.

Incorrect. A t distribution with 3 degrees of freedom has a larger spread than the standard Normal distribution.

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Correct. The larger the degrees of freedom for a t distribution, the close its density curve is to the standard Normal curve.

Incorrect. The larger the degrees of freedom for a t distribution, the close its density curve is to the standard Normal curve.

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Correct. A t distribution with 5 degrees of freedom has a larger spread than a t distribution with 14 degrees of freedom.

Incorrect. A t distribution with 5 degrees of freedom has a larger spread than a t distribution with 14 degrees of freedom.

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Correct. Because s is an estimate σ, it has error or variability. As a consequence, the t used in inference has to be more spread out than the standard Normal used when we know the value of σ.

Incorrect. Because s is an estimate σ, it has error or variability. As a consequence, the t used in inference has to be more spread out than the standard Normal used when we know the value of σ.

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Correct. This is a true statement.

Incorrect. This is a true statement.

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