|1. What is the 68-95-99.7 Rule?|
Explain the 68-95-99.7 Rule in your own words (I’ll be able to spot Googled answers; do not use Googled or internet searched answers).
How is this going to be helpful to us in statistics? (Imagine we could make the whole world standard Normal.) Are there other (probability) rules like this that can guide us?
Don’t over think this, and give an example or two…. Don’t try to cover the entire topic in one posting…. Leave room for your classmates to add in.
|2. Convenience Sampling vs. Random Sampling|
In discussions of probability, there is a lot of talk about samples.
What makes a good sample? Is there generally considered an “ideal sample size” by statisticians? Is bigger always better? Is a sample of 1 ever enough? What important characteristic are statisticians looking for in their samples, when it comes to making inferences?
For example, given the choice to answer a question from New York City residents about their opinions on the placement of a Mosque near Ground Zero, would you prefer a call-in poll from 4,354 viewers from NY1 (a NYC news station), or a random poll of 30 NYC residents? Why?
|3. Tools for Normal Distributions and How to Calculate Z-Scores|
WARNING students, this question is long, and will require calculations!
In this class, you need to get comfortable transforming statistics into Z-scores (and soon t-scores), and then calculating the probability of being above or below that score, or between two scores. You will practice this in this week’s assignment.
Many tools are available on-line to help understand normal distributions, how to come up with standardized values (z-scores), and how to find probabilities associated with various z-scores (aside from using the standard normal table). Two examples are the following websites: http://ncalculators.com/statistics/z-score-calculator.htm,
Think of the growth charts when you went to the doctor as a child. What percentile were you in? What percent of your age group were below you or above you? What percent were between you and the average? These are the types of calculations we need to do with Z-(or t-)scores. We will translate any value into its distance from the mean, plus or minus, and then we can say what percentile it is. 50% will be below the mean, and 50% above in our normal curves.
Compare scores in your textbook to what you get with these tools. Once you have them figured out, you should be able to use these to help with homework.
Let’s take some time to practice online, together.
Going back to the height example, it turns out that in the U.S. the average height for men is about 69 inches, and 64 inches for women. Both have a standard deviation of about 3 inches (these stats actually vary by ethnicity, age, and other variables.)
My height is 68.75 inches (I’m counting every little bit, as my son is already passing me).
Using Excel’s function =standardize(x, mean, s.d.), I find that my height is -0.0833 standard deviations below the mean: =standardize(68.75, 69, 3); this is my Z-score! (I am ever so slightly below the mean.)
Using Excel’s =normdist(x, mean, s.d.) function, I find that 0.4668 (or 46.7%) or men are below my height. This means that 1-.4668 = .5332 are taller than I, including my son.
For example, using the zscorecalculator, I select “Left” and enter -0.08 in the left zscore. I get the value of 46.81%. (It is not quite as precise as Excel.) Note the chart below showing all the people in my height category or less. If I hit the “Right” button, and enter the same figure, I get 53.19%.
Try also clicking “Middle, equal area” with the standard deviation score of -1, and you should get back 68.27 (according to the 68-95-99.7 Rule)! Plug in a 2, just for fun.
When working these problems, be sure to draw a graph first, and then compare your drawing to the results from these tools. Check your math with the textbook or Excel if you have any doubts.
While it is unlikely you will ever be asked to calculate a z-score in your professional life, unless you decide to become an data analyst, these are at the foundation of inferential statistics, and it is critical you understand what they mean. We know the odds of a fair coin. These exercises teach you the odds of a normal curve.
Now it’s your turn. Can you tell us what is your height “z-score” and the percent of people who rank lower than you, or between you and the mean?
[ Link to my textbook – https://email@example.com:41.6 ]