Get us back into the swing of things:
Problem Number 1: Newts and Healing
"Biologists studying the healing of skin wounds measured the rate at which new cells closed a razor cut made in the skin of an anesthetized newt. Here are the data from 18 newts, measured in micrometers (millionths of a meter) per hour:
29 27 34 40 22 28 14 35 26 35 12 30 23 18 11 22 23 33
What do we believe the average healing rate of a newt is?
What formulas do we need?
What information is given -- and what isn't?
What is a good confidence level for us? Find those values.
Problem Number 2: Newt Salve
I've created a Salve that I think will help newts heal faster than previously. So I anesthetized some more newts, cut them, applied the salve and took some recordings. Here they are:
23 27 31 39 27 23 42 30 30 44 18 28 32 28 28 29
How can we see whether or not the salve made a difference?
HYPOTHESIS TESTING!
set null hypothesis
Always equal to.
Always AGAINST what you want to prove.
Always the status quo.
set alternate hypothesis
one or two tail test?
Do we care if DIFFERENT ... (not equal to)
or > < ?
set alpha level
what percent sure do we want to be that we are correct?
check data (if possible)
outliers with appropriate methods
check shape of data, etc.
bimodal is a big problem.
run analysis (get z-score, p-score)
compare and analyze
Problem Number 3: Smarter than your average Third Grader
A school district is trying to prove that they have smarter third graders than the average. One way to do that is to look at the scores on a nationwide test. On this test, the national mean is 32, and the sd is 11. Below are the scores for 45 students in the district. Consider the scores an SRS of the third grade population.
40 26 39 14 42 18 25 43 46 27 19 47 19 26 35 34 15 44 49 38 31 46 52 25 35 35 33 29 34 41 1 49 28 52 47 35 48 22 33 41 51 27 14 54 45
Problem Number 4: Ancient Air
The composition of the earth's atmosphere may have changed over time. To try to discover the nature of the earths atmosphere long ago, we try to examine the gas in bubbles inside the ancient amber. The gas has been trapped (by estimates at least) an average of 75 to 95 million years.
Below is the percent of nitrogen that is stored in these samples air bubbles:
63.4, 65.0, 64.4, 63.3, 54.8, 64.5, 60.8, 49.1, 51.0
The air currently has a percent of 78.1 nitrogen. [according to wikipedia]
Problem Number 5: It's Electric!
Here are 6 measurements of the electrical conductivity of a liquid: 5.32, 4.88, 5.10, 4.73, 5.15, 4.75.
The liquid is supposed to have a conductivity of 5.
The measurements above are an SRS from the population. The population has sd of 0.2
This liquid is used to help insulate circuits. As such, we need to make sure that it has an average conductivity of 5--if it does not, we cannot use it for the intended use. Run a hypothesis test to see if we can use this liquid for it's intended purpose.
Data Throwdown. "The Worst Chart in the World".
So look at this graph--my favorite of the bunch:
there's so many things wrong with it I'm not even sure where to start. But what's astounding about it is that it almost looks good! But it's not.
...and oh wow:
...ok, ok, one more, but more subtle: http://i.imgur.com/diP37Zy.jpg
... ok, ok one more, wrong for MANY reasons: http://www.ritholtz.com/blog/wp-content/uploads/2009/11/best-pie-chart-ever.jpeg
Your goal: create a terrible graphic using some set of data. Use all the bad tricks in the book if you want -- 3D graphs, univariate as a time plot, axes that don't match, truncate axes ... whatever.
https://consultantsmind.files.wordpress.com/2012/12/bad-graph-no-axis1.png?w=473&h=230