t-Distributions

T-distributions represent a critical aspect of probability distribution frequently employed in the field of statistics. They bear similarity to normal distributions, with the key difference being their thicker tails, which accommodates greater variability. The significance of t-distributions becomes more evident when we work with smaller sample sizes or when the population standard deviations are not known.

Finding a t-Value for a Confidence Level

A sample of 15 students took a calculus test, and the average score was 70 with a standard deviation of 10. What is the t-value for the 95% confidence level?

Finding the Critical t-Value

In an experiment involving a t-distribution, we have a sample size of 15 and we want to find the critical t-value for a two-tailed test with a significance level of 0.05. What is the critical t-value?