Lab Exercise
- Author:
- Timo Budarz
Practice with GeoGebra
This lab will focus on making you familiar with GeoGebra with an emphasis on statistics that will be useful for us in the future.
PROCEDURE
- Choose the probability calculator from the view menu. Leave it on normal (Gaussian) distribution.
- Choose a mean value of 1.5 and a standard deviation of 0.5. Q1:What fraction of a population should fall between values of 1.0 and 2.0?
- Q2: What fraction should fall between 1.5 and 2.0?
- Q3: What fraction should fall between mean +/- two standard deviations? 1.96 standard deviations? This is related to our 95% confidence interval, often denoted CI. In this context we would expect 95% of a sample to fall in this range. Likewise a new data point would have a 95% chance of falling in this range.
- Open the spreadsheet view from the view menu. Enter in a column these values: 1.94, 1.89, 1.77, 1.89, 1.69, 1.91. You might imagine that these represent the period in seconds of a pendulum that swings in a doorway and is measured multiple times by hand.
- In an adjacent cell type
=mean(A1:A6)and hit enter. (If you used different cells, then use the appropriate cell indices.) It's a good idea to label cells, so write mean next to that cell. Calculate the standard deviation of the data set in another cell by typing=SD(A1:A6). Label this cell as well. - Notice that the cells might have inconsistent numbers of significant figures. Under the options menu you can select rounding and choose a number of significant digits or decimal places. Even though this is possible, it may be necessary to modify values appropriately for lab reports. For now, choose 5 significant digits.
- Within the probability calculator window, choose the tab labeled statistics. In the drop down menu choose Z Estimate of a Mean. Enter the appropriate values in the cells (use a 0.95 confidence level) and write down the value you should report along with its error from the bottom of the list. Make sure to follow the rules mentioned in this chapter when deciding which digits to keep. If you don't see enough digits, adjust the rounding. If you have too many, decide by hand what to keep. Q4: What is the correct way to write this result and associated error? Realize that when estimating a mean, we are not speaking of fractions of a population falling within a certain range, etc. Instead we are saying that there is a 95% probability that the TRUE mean of the dataset lies within the range you wrote down. The error on that range will decrease as you acquire more data points in proportion to . This is not true of a standard deviation, only of standard error.