T-Distribution

The 𝑡-distribution is bell-shaped and symmetric about 𝑡 = 0, similar to the normal distribution.

• Characteristics of a 𝒕-Distribution

• Conditions in Using the 𝑡-Distribution

The total area under a 𝑡-curve is 1 (or 100%, similar to the normal distribution).

• Characteristics of a 𝒕-Distribution

• Conditions in Using the 𝑡-Distribution

The mean, median, and mode of the 𝑡-distribution are all equal to zero

• Characteristics of a 𝒕-Distribution

• Conditions in Using the 𝑡-Distribution

• Conditions in Using the 𝑡-Distribution

• Characteristics of a 𝒕-Distribution

The 𝑡-distribution is a family of curves, each determined by degrees of freedom.

• Characteristics of a 𝒕-Distribution

• Conditions in Using the 𝑡-Distribution

As the sample size 𝑛 gets larger, the 𝑡-distribution gets closer to the normal distribution.

• Characteristics of a t-Distribution

• Conditions in Using the t-Distribution

The sample is small (𝑛<30) and randomly selected.

• Characteristics of a 𝒕-Distribution

• Conditions in Using the 𝑡-Distribution

The population standard deviation 𝜎 is unknown.

• Conditions in Using the 𝑡-Distribution

• Characteristics of a 𝒕-Distribution

The parent population, the population from which you are sampling, is essentially normal.

• Characteristics of a 𝒕-Distribution

• Conditions in Using the 𝑡-Distribution