Question
There are 100 students in a class. Let the random vaiable (X) represent the weight of each student. The average weight of all students in the class is 200 lb., with a standard deviation of 40lb. Assume that we repeatedly take samples of twenty-five (25) students to estimate the average weight of all the students in the class. With each sample, we compute a sample mean.
What is the average value of all possible sample means?
What is the standard deviation of all these sample means?
Answer
1. Average value of all possile means will be approximately equal to the 200 lb estimate obtained from the larger (100) sample.2. See the formula for the Standard-Error, which doubles, when you reduce the sample-size to 25%. I.e. going from large sample of 100 students to small samples of 25 students will increase the SD to 2x40 (original is 40) = 80 lb.Note: Both of those questions relate to central limit theorem and you acn see the tools (Java applets) and the class notes available under:http://socr.stat.ucla.edu/for more detailed explanation. http://socr.stat.ucla.edu/ http://vrd.askvrd.org/services/answerschema.xml
