Would greatly appreciate any help on this homework question, I will post my answers to parts a) and b) underneath as well but I don't think they are correct.Thanks!
a) Take 10 different samples of 20 scores from the normal distribution with a mean of 125 and a standard deviation of 15. Find the mean of each sample and display them.
pnorm(0.5, 125, 15) [1] 5.20557e-17
b) Now take 10 different samples of 100 scores from the normal distribution with a mean of 125 and a standard deviation of 15. Find the mean of each sample and display them.
pnorm(0.1, 125, 15) [1] 4.157522e-17
c) Describe and explain the differences between the two sets of sample means.
Imagine that you work in a factory that makes thousands of cupcakes each day. The cupcakes are supposed to weigh 125g each and the distribution of the weight is supposed to be Normal with mean 125 and standard deviation 15.
Now imagine that each day you randomly select 20 cupcakes from all of the cupcakes that were made that day. This is a sample of size 20. Weigh each of the cupcakes in that sample and find the mean of the sample.
If you did this for for ten consecutive days, you would end up with ten samples of size twenty. In part A of your question, you are asked to write some computer code (which language?) to simulate this experiment. Write some code that creates ten samples, each sample having 20 observations, and find the average of each sample.
In part B you are asked to do the same thing but each day you select a random sample of 100 cupcakes, weigh them and find the average weight. Again, you do this for ten days in a row.
In part C, you are asked to compare the ten averages that you calculated in part A with the ten you calculated in part B. You should see that the ten averages in part B area "more tightly grouped together" than the ten in partA. That is, the standard deviation of the ten averages in part B will be smaller that the standard deviation of the ten averages in part A.
You will need to find or write a function that generates observations (scores) from the normal distribution. Can you take it from here?