Level of Confidence?

Here is a question I received from a student by e-mail.

“Could you clraify exactly what it means to estimate the level of confidence of our conclusion. What is our conclusion on (which part of the guide) and how are we to estimate the level of confidence of the conclusion if it is a written statement.”

“You are trying to answer the question:

‘Is there a significant difference between the number of counts/minute detected when the nu-salt is present compared to when the nu-salt was not present?’

You need to use the statistical quantities we measured for the number of counts/minute both with and without the nu-salt present: average, standard deviation, number of counts and standard deviation of the mean. The level of confidence will depend on how far apart the averages of the two experiments are compared to the standard deviations of the means.”

In other words, if the means differ by about 1 SDM then you can conclude that the difference is real to a 68% level of confidence. If they differ by 2 SDM then they differ to a 95% level of confidence.  If they differ by something between 1 SDM and 2 SDM  then you conclude that the difference is real to something between 68% and 95% level of confidence.

Unit 2 Bugs

On WebCT there is an Activity 2-11 upload but there is no Activity 2-11.  That was something I forgot to delete after I revised Unit 2 last year. It is not there now and is not due — don’t worry about it.   Furthermore, there is no SP2-4 and SP-5, yet.

(I was thinking about assigning a problem on calculating the probabilities of all possible outcomes of throwing three dice, but I wonder if that would be too hard?)

This is a copy of a class email.

The Standard Deviation vs Standard Deviation of the Mean…

Today we encounered the concept of the Standard Deviation. The Standard Deviation of the Mean is coming tomorrow. Understanding the distinction is a real brain teaser, but important.

There’s a lot to do tomorrow so we’ll try not to waste so much time at the beginning of class. One source of random numbers is radioactive decay.  I’ll show how some common stuff you can get in the supermarket has radioactivity significantly above the background level.

Bowling Data

The bowling data serve as grist for plotting a graph using Excel. One of the homework problems is to superimpose a mathematical model. To ease this task there is a downloadable spreadsheet file called the “Modeling Worksheet”. (Look on WebCT under Unit 1.)  Another spreadsheet file, the “Modeling Tutorial”, shows an example of how to use it.

 The Modeling Tutorial Spreadsheet

The model you’ll want to use is

x0 is the intercept (b, cell C2) on the vertical axis and vavg is the slope (m, cell C1).  The position of the ball is x(t) and the time from the start is t.

(This model ignores the slowing of the ball as it rolls.)

You can use the Modeling Tutorial spreadsheet as a template for assignment problem SP1-2
To enter in this formula, you type in the first cell of y-theory (cell C8)

=$C$1*A8 + $C$2

You should see the theoretical value for the first data point calculated in cell C8. If you made a mistake there’s an error message and you’ll have to fix it before going on.

Copy this formula down the column to the end of the data.  A8 will change to A9, A10, etc but the references to $C$1 and $C$2 do not change because placing the dollar sign in front of the column letter and row number makes these references Absolute References instead of Relative References. After you copy the formula a line should appear on the graph representing the theoretical model.

Now you need to change the numbers in cells C1 and C2 until the line passes through the data points so that it represents a reasonable model of the position vs time which is consistent with the data.

(I know there is an automatic “Trendline” feature in Excel, but you should do the procedure described here so that you can understand and appreciate the automatic process better.)

Asteroid Buzz

You probably didn’t notice but two small asteroids came close to Earth on Wednesday. (http://www.nasa.gov/topics/solarsystem/features/asteroid20100907.html).
Their orbit took them within the moon’s orbit of the earth. Small means 10 to 20 m in diameter.
 Image credit: NASA/JPL-Caltech

This apparently happens all the time but until recently we didn’t know. The rate of asteroid detection has escalated recently as shown by this movie:

Asteroid Discovery From 1980 – 2010

Most of those asteroids are pretty far from Earth, but there are a lot  too close for comfort.

Ignorance was bliss.

PS: This will not be on the exam.

First Day was O.K.

Because I wore my rain jacket and left the sunglasses at home the weather cleared up.  Both classes were able to go to Holland park and pitch the baseballs in the sun — even the grass wasn’t wet.

A cellphone video of the baseball activity.
The main point of this exercise was to get some practice using a spreadsheet to analyse data. Homework SP1-1 requires averaging the data, finding the minimum and maximum speed and sorting. I found out that Firefox changes tabs to spaces in text files so that you can’t just copy and paste the data. Using “Paste Special”.. “text” does the job the most easilty. Alternatively you can paste data and then use the “Text to Columns” feature.
Friday we bowl. It’s going to rain Friday, I’m sure, even if I wear all my rain gear. So it’s good that we do that in doors in our Studio room not the bowling alley, unfortunately. Then we’ll learn how to make a graph in Excel.
One can also do these exercises in OpenOffice if one wants their own capable speadsheet application which is reasonably compatible with Excel.  There are a few differences, especially when it comes to graphics, but free is good.

2 days to go

It’s Labour Day Weekend and the Schedule is set, WebCT configured and the handouts printed.  The only question is the weather on Tuesday.  The first day is the only day we do something outdoors and reports show rain is possible. Normally we go outdoors and measure how fast we can pitch a baseball.  Alternative activities are now being contemplated.

I’ve just learned from a student that the Chemistry 121 exam in Burnaby is just before the Physics 140 exam in Surrey.  There may be several students afflicted by this scheduling fiasco, so we’ll have to make some provision.

This is the first post on the Physics 140 blog.  I’m still configuring the WebCT container and figuring out the semester’s schedule.  There’s only a little more than a week until we start and I’m wasting time starting this blog. So much for efficiency.