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LOS i: Describe the properties of Student's t-distribution and calculate and interpret its degrees of freedom.

Which statement best describes the properties of Student’s t-distribution? The t-distribution is:

A)	skewed, and defined by a single parameter.

B)	symmetrical, and defined by two parameters.

C)	symmetrical, and defined by a single parameter.

The t-distribution is symmetrical like the normal distribution but unlike the normal distribution is defined by a single parameter known as the degrees of freedom.

Which one of the following statements about the t-distribution is most accurate?

A)	The t-distribution approaches the standard normal distribution as the number of degrees of freedom becomes large.

B)	Compared to the normal distribution, the t-distribution is more peaked with more area under the tails.

C)	The t-distribution is the appropriate distribution to use when constructing confidence intervals based on large samples.

As the number of degrees of freedom grows, the t-distribution approaches the shape of the standard normal distribution. Compared to the normal distribution, the t-distribution is less peaked with more area under the tails. When choosing a distribution, three factors must be considered: sample size, whether population variance is known, and if the distribution is normal.

When is the t-distribution the appropriate distribution to use? The t-distribution is the appropriate distribution to use when constructing confidence intervals based on:

A)	large samples from populations with known variance that are nonnormal.

B)	small samples from populations with known variance that are at least approximately normal.

C)	small samples from populations with unknown variance that are at least approximately normal.

The t-distribution is the appropriate distribution to use when constructing confidence intervals based on small samples from populations with unknown variance that are either normal or approximately normal.

Which one of the following distributions is described entirely by the degrees of freedom?

A)	Student’s t-distribution.

B)	Normal distribution.

C)	Lognormal distribution.

Student’s t-distribution is defined by a single parameter known as the degrees of freedom.

With 60 observations, what is the appropriate number of degrees of freedom to use when carrying out a statistical test on the mean of a population?

When performing a statistical test on the mean of a population based on a sample of size n, the number of degrees of freedom is n – 1 since once the mean is estimated from a sample there are only n – 1 observations that are free to vary. In this case the appropriate number of degrees of freedom to use is 60 – 1 = 59.