MATH 220 Lecture Notes - Lecture 7: Potato Chip, Simple Random Sample, Point Estimation
Document Summary
Objective #1: describe the properties of the student"s t distribution. In section 7. 1, we showed how to construct a confidence interval for the mean of a normal population when the population standard deviation is known. The critical value is because the quantity has a normal distribution. It is more common that is unknown. When we don"t know the value of , we replace it with the sample standard deviations (s). However, we cannot then use as the critical value, because the quantity does not have a normal distribution. One reason is that s is, on the average, a bit smaller than , so replacing with s tends to increase the magnitude. Another reason is that s is random whereas is constant, so replacing with s increases the spread. The distribution of this quantity is called the student"s t distribution. It was discovered in 1908 by william sealy gosset. Degrees of freedom for the student"s t distribution.
