STRAIGHT STATISTICS

Confidence Interval for the Mean (σ Unknown or n<30)

In many situations, the population standard deviation is not known and the sample size is less than 30. t-distribution must be use when the sample size is less than 30 and the variable is normally or approximately normally distributed.

Characteristics of t-distribution:

1. It is a bell-shaped.
2. It is symmetrical about the mean.
3. The mean, median and mode are equal to 0 and are located at the center of the distribution.
4. The curve never touches the x-axis.
5. The variance is greater than 1.
6. The t-distribution is actually a family of curves based on the concept of degrees of freedom, which is related to sample size.
7. As the sample size increases, the t-distribution approaches the standard normal distribution.


Degrees of Freedom- are the number of values that are free to vary after a sample statistics has been computed, and the tell the researcher which specific curve to use when a distribution consists of a family of curves. Denoted by d.f.