Lesson 6
1. Lesson 6
1.4. Explore 3
Module 4: Statistical Reasoning
If you perform a survey or experiment only once, you cannot have much confidence that you can repeat the survey or experiment and get the same results. The more you repeat the survey or experiment, the more confidence you will have in predicting the results of the next survey or experiment.
Consider a high school with 250 students in Grade 12. If you ask one student what theme song he or she wants for graduation, you can’t have any confidence that you will receive the same answer when you ask a second student. If, however, you have asked 100 students and 80 of them picked the same song, you can have increased confidence that 8 of the next 10 students you ask might pick the same song.
There is a demo posted online that shows the connection between levels of confidence and sample size. To explore the demo, put the following keywords into your favourite search engine: “The diagram below illustrates a series of tests—each unique in terms of test data—that are run on a system.”
Using those keywords, you should find a link to a website that explores “Level of Confidence” and its connection to sample size. At the bottom of the website page is a simple simulation. If you cannot find this website through your search, contact your teacher for assistance.
The simulation, which is provided near the bottom of the website, shows a line segment dropping down to the normal curve at different spots to replicate a series of tests to determine the level of confidence. To get a full explanation of how to use the demo, choose “Instructions For Using This Demo.”
Important features to note:
- To change the sample size, left-click once to increase the sample size by 50 each time. Double-click to get the sample size back to 50.
- To change the confidence level, right-click and the level will increase 5% each time. The default confidence level of the test is 75%, so right-click four times to get a 95% confidence interval.
- A catch occurs when the falling red bar includes the mean.
- A miss occurs when the falling red bar does not include the mean.
- The width of the red bar is the confidence interval.
- Each time you click, you reset the simulation.
Watch the simulation. Notice that the total number of tests, number of catches, number of misses, and “% of catches so far” changes the longer you let the demo run.
- When you first start the demo, how close are your experimental results (% catches so far) to your confidence level?
- As the simulation goes on, what do you notice about these two values?
- Does the number of trials affect the outcome for the level of confidence?
Self-Check 2
