module 20 distribution of sample means 9 of 12 is the size of the population important notice that the size of the population is not mentioned in our discussion of the center spread and shape of the sampling distribution for sample means from our previous discussion we know the following the mean of the distribution of sample means is the population mean mu the standard deviation of the of the distribution of sample means is Sigma ided by a squ root of n where Sigma is the population standard deviation of individual measurements the larger the sample size n the smaller the standard deviation in other words the means from larger samples have less variability so large samples give more accurate estimates of the population mean the shape of the distribution of sample means is approximately normal when n is greater than 30 this is true even when the variable has a skewed left distribution for individuals in the population if the variable is normally distributed in the population then the distribution of sample means will be normal regardless of the sample size these statements are true regardless of the sample size of the population as long as the population is large in this course we work only with large populations to illustrate this point we compare distributions of sample means from two populations of different sizes population a has 10,000 newborns population B has 20,000 newborns for each population the mean and standard deviation of individual birth weights is the same the mean is 3500 and the standard deviation is 500 to create the sampling distribution we selected 525 random samples of 100 babies from each population and made a histogram of the sample means we did this twice for population a so two of the history Rams represent 525 samples from the same population as expected there are some differences in the samples collected due to random chams comparing these two histograms gives us a sense of how much variation we can expect from the process of selecting random samples notice that the histogram of sample means from a larger population B has a similar shape Center and spread to the histograms from population a the size of population B did not affect the sampling distribution so here we have population a and this second one is also from population a the third one is from population B so notice the size of the population B did not affect the sampling distribution so what's the main point the size of the population does not affect the variability of the sample means size matters if we are talking about sample size from random samples B size does not matter if we are talking about population size as long as the population is large