![]() ![]() ![]() Note: If n is large, then t is approximately normally distributed. Has a t distribution with (n-1) degrees of freedom (df) If X is approximately normally distributed, then As the degrees of freedom increase, the t distribution approaches the standard normal distribution. There are actually many t distributions, indexed by degrees of freedom (df). However, we can estimate σ using the sample standard deviation, s, and transform to a variable with a similar distribution, the t distribution. If the standard deviation, σ, is unknown, we cannot transform to standard normal. How will this affect the standard error of the mean? How do you think this will affect the probability that the sample mean will be >22? Use the Z table to determine the probability. So the probability that the sample mean will be >22 is the probability that Z is > 1.6 We use the Z table to determine this:Įxercise: Suppose we were to select a sample of size 49 in the example above instead of n=16. Suppose we draw a sample of size n=16 from this population and want to know how likely we are to see a sample average greater than 22, that is P( > 22)? If the standard deviation, σ, is known, we can transform to an approximately standard normal variable, Z:įrom the previous example, μ=20, and σ=5. If X has a distribution with mean μ, and standard deviation σ, and is approximately normally distributed or n is large, then is approximately normally distributed with mean μ and standard error. The statistic used to estimate the mean of a population, μ, is the sample mean. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |