- Simulate making 25 observations from a population whose mean is 100 and standard deviation is 15 (i.e. N[100,15])
- Compare the sample mean (x-bar) to the population mean (mu).
- Compare the sample std. dev. (s) to the population std. dev (sigma).
- Begin building a table with three headings: "Sample Number", "Sample Mean", and "Sample Std. Dev." and record your first simulation.
- Repeat the procedure until you have simulated taking a sample of 25 observations 20 times.
- Now make a stem plot of the 20 means.
- Is it skewed or semetric? Where is its center?
- What is the mean of the 20 means? Is it different from the population mean?
- What is the std. dev of the 20 means? Is is different from the population std. deviation?
- Compute the population std. dev. (sigma) divided by the square root of the sample size (n=25)
- How does this compare with the the standard deviation of the 20 means?
- Make find the "z-score" of each of the 20 sample means to make a Normal
Probability Plot. Is the plot linear? What does this imply?
- Make a prediction about simulating taking a sample of 16 observations from a population normally distributed N[50,12]. What would the sample mean look like? The sample std. dev?
- Have the computer simulate this...how does it compare with your prediction?
- Do this 19 more times (Make a new table). What do you think the mean of the means will be? What do you think the standard deviation of the means will be?
- How did your prediction compare with your 20 simulations of sampling an N[50,12] with sample size n=16?