Question: Explain why a t distribution is associated with n - 1 degrees of freedom and describe the information that is conveyed by the t statistic.

• The t distribution is a normal-like distribution with greater variability in the tails than a normal distribution because the sample variance is substituted for the population variance to estimate the standard error in this distribution.

• The t distribution is a sampling distribution for t statistic values that are computed using the sample variance to estimate the population variance in the formula. As sample size increases, the sample variance more closely estimates the population variance_ The result is that there is less variability in the tails of a t distribution as the sample size increases. Each t distribution is associated with the same degrees of freedom as sample variance for a given sample: df = n - 1.

• The t statistic is an inferential statistic used to determine the number of standard deviations in a t distribution that a sample mean deviates from the mean value or mean difference stated in the null hypothesis.