If a population is known to be normally distributed with µ=250 and the standard deviation is 40, what will be the characteristics of the sampling distribution for the sampling mean based on a random sample size of 25 selected from the population?
Some textbooks don't always provide the correct criteria for choosing.
It is just edition nine that Triola says "In chapters 6,7, and 8 there is a change from "n>30" to "sigma known" as a key criterion for choosing between the normal and t distributions..."
Triola's t table,by the way,goes up to df=2000 not as in earlier editions up to n=30.
It's a general principle applicable to any distribution with a finite variance. Look in a chapter that discusses sampling distributions, that is, the sampling distribution of the sample mean from any distribution. Or consider that the variance of the sum of independent random variables is the sum of the variances, and that multiplying a variance by a constant gives you the square of the constant by the variance.
Statistics/Sampling distribution of the mean
Posted - 10/27/2009 : 19:27:59
