Answer:
The t-score has the same interpretation as the z-score. It measures how far in standard deviation units \stackrel{-}{x} is from its mean μ. For each sample size n, there is a different Student’s t-distribution. The degrees of freedom, n – 1, come from the calculation of the sample standard deviation s. Remember when we first calculated a sample standard deviation we divided the sum of the squared deviations by n − 1, but we used n deviations \left(x-\stackrel{-}{x}\text{values}\right) to calculate s. Because the sum of the deviations is zero, we can find the last deviation once we know the other n – 1 deviations. The other n – 1 deviations can change or vary freely. We call the number n – 1 the degrees of freedom (df) in recognition that one is lost in the calculations. The effect of losing a degree of freedom is that the t-value increases and the confidence interval increases in width.
Properties of the Student’s t- Distribution 0.05, 95% level of confidence, we find the t-value of 1.96 at infinite degrees of freedom.
Explanation: