The Quick rule of approximation: 68 - 95 - 99.7
1) Confidence interval:
Newts:
Some newt data (from The Basic Practice of Statistics, by David Moore):
Biologists studying the healing of skin wounds measured at 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
We know from previous experiments that the sd for newts healing is 8 micrometers per hour.
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]
2) p-value:
cutting newts with NEWT SALVE 2000!
I have created this amazing newt salve, called NEWT SALVE 2000. It is supposed to help newts heal at a faster rate than they did before. Here are the healing times:
23 27 31 39 27 23 42 30 30 44 18 28 32 28 28 29
The big question becomes--do I know that this data actually shows that the newt salve does work? I can't know if the difference is in the population itself that I chose at random, the things I chose, or just because these newts were having a good day.
And so I set up some hypothesis testing.
We've done a study to see if the resting rate at which people burn calories increases after they've done a exercise regimen. We found the average rate of caloric burn in subjects before (over a two week period) and then had them exercise every morning for two weeks. We collected that data as well. the sd.pop = 250. The data we collected is in the lists below.
Can we say that people burned more calories after the workouts then when they were not exercising?
THIS IS A MATCHED PAIRS DESIGN. BE CAREFUL. IF YOU ARE UNSURE OF WHAT TO DO HERE, PLEASE COME TALK TO ME AND MAKE SURE YOU'RE DOING IT RIGHT.
make sure to run a full analysis
calories.burned.before
1679 1039 1952 1187 1626 1698 1140 1581 1887 1171 1345 1722 1253 1183 1205 1572 1099 1699 1330 1356 1249 1337 1731 1635 1483
calories.burned.after
1814 1223 2089 1334 1691 1822 1115 1656 1881 1151 1388 1873 1257 1097 1405 1672 1205 1708 1497 1365 1149 1413 1749 1591 1423
3) stop watch names
plotting bivariate data
explanatory vs. response
independent vs. dependent
what is correlation
picture from wikipedia: http://upload.wikimedia.org/wikipedia/commons/d/d4/Correlation_examples2.svg
guess the correlation
correlation and point calculator: http://illuminations.nctm.org/Activity.aspx?id=4186
sites used in class:
correlation vs. causation picture
4)