Exploring Normal Distributions</SPAN>
The purpose of this problem is to investigate the behavior of the means and standard deviations of repeated samples of size 25 taken from normal distributions. The TI graphing calculator (and most other graphing calculators) has the ability to generate values of variables from various distributions, including normal distributions with specified mean and standard deviation. For this investigation you will obtain 25 observations from the N(100, 15) distribution, and calculate certain descriptive measures for these observations. You will repeat this procedure a number of times and then study the results. Procedure: Here are the steps for carrying out your investigation with the TI-83 (if you have another version you should check you users manual).
1. Generate 25 random numbers from a normal distribution with a mean of 100 and standard deviation of 15 and put these numbers into list L1. This is done by going to the home screen (nothing on the screen but a blinking cursor) and pressing the MATH button. Press the arrow button until PRB is highlighted then use the down arrow to highlight RandNorm. Press Enter so that RandNorm( appears on the home screen. Enter the mean, standard deviation, and number of random numbers by entering 100,15,25. Then have these data values entered into L1 by using STO L1. Your home screen should then have RandNorm(100,15,25) --> L1. Press enter then go to the list to see that 25 numbers (all fairly close to 100) was entered into L1.
2. Now calculate one-variable statistics on this data. This can be done using One-Var Stat on L1. To do this, press the STAT button while at the home screen. Arrow over to CALC and choose the first option, One-Var Stat. By default your calculator will use L1; however, I would get in the habit of always specifying which list to do statistics on, so press 2nd then 1 so L1 pops up after One-Var Stat. When your home screen reads One-Var Stat L1, press enter. For this activity, you will be using the sample mean and the sample standard deviation (Sx).
3. Compare the sample mean,
for the 25 data values with the population mean, m = 100, and compare the sample standard deviation,
to the population standard deviation, s = 15. Begin building a table with these headings:Sample Number
Sample Mean
Sample Standard Deviation
This table can be entered in Excel to ease data entry for future steps. Record the mean and standard deviation for your first sample of 25 observations.
4. Repeat steps 1-3 until you have 20 samples from the N(100,15) distribution (this will take some time). Each time, put the 25 observations in L1, compute one-variable statistics on your sample, and record the mean and standard deviation in your chart. (Hint: You can quickly do this using 2nd, Enter in your calculator.)
I'm grateful for any help I receive. Thanks in advance!
-- Yaroslava
