Lesson 7
1. Lesson 7
1.3. Explore 2
Module 4: Statistical Reasoning
The data gathered by quality control departments from sampling drug capsules, cereal boxes, or ultimate discs is all done through random sampling. Capsules, cereal boxes, and ultimate discs are taken throughout the day and tested to create the data that companies use to make decisions about quality control. If a company chooses to take its entire sample at one time and from one machine, the company may not get a realistic picture of what is happening in the entire production facility. The level of confidence in a set of data relies in part on random sampling.
Consider the following situation.
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Angelica’s favourite sport is hockey, and she plays in a competitive league. Suppose she wants to know what sport teenagers in her area like to play most. She decides to ask her friends on Facebook. After 2 h, 45 of her friends have replied. Most of her friends have chosen hockey as their favourite sport to play. Is this a random sample? How reliable are these results? Do these results accurately reflect the population of teenagers in Angelica’s area?
Since Angelica plays hockey, it is likely that many of her Facebook friends are from some of the hockey teams she has played on in the past. This sample does not accurately reflect the views of all of the teeenagers in her area. This is not a random sample, so these results are not very reliable and you should have limited confidence in them.
Now suppose Angelica wants to improve the reliability of these results. Since all of her closest friends have already replied, she decides to ask the students in her homeroom class. Out of the 25 students in her class, 18 of them choose rugby—surprisingly, they are all on the rugby team. What does this do to the confidence in the first result? It definitely does not support the original results.
If Angelica really wants to know what sport teenagers in her area like to play the most, she will need to look at how she could randomly choose people to answer this question so that her results are reliable and she could have a high level of confidence in the results. Perhaps she could randomly ask students in her school by using class lists from the office and picking every fourth person on the list. This would allow her to ask 25% of the student population. She would then have a much higher level of confidence in the results and could make some accurate predictions about what sport most teenagers in her area enjoy playing. In fact, any random method to generate this data would help improve the level of confidence in the results.
Once results are gathered from a random sample, the results can be generalized to the population. You can have a very large random sample or have a lot of smaller random samples where you combine the results. If you do not have a random sample that is large enough, then the margin of error and confidence interval may be too large and you cannot accurately generalize the results to the population. Statisticians can use small sample sizes, as long as the sample is truly random. If the sample is not random, the results cannot be accurately predicted for the entire population and the confidence intervals are unreliable.
Did You Know?
In March 2011, Ipsos Reid conducted the Social Media and Political Engagement Study. The intent was to measure actual potential voter use of social media and traditional media during the 2011 federal election campaign. Many in the media had predicted that the 2011 federal election campaign would be the first social media campaign in Canadian political history.
The survey results show that one-fifth of Canadians (21% or 5 154 000 potential voters) engaged through social media or traditional news media web sites to debate public policy or discuss political issues. Of these 21% of potential voters, respondents between the ages of 18 and 34 are most likely to say they are engaged on a weekly basis. However, it’s the middle-aged and older Canadians who engage on a daily basis in these political discussions on social media.
When respondents were asked where they go when they discuss public policy and political issues online, there was a fairly even split between new media sites (net: 18%) and traditional media sites (net: 15%).
A randomly-selected sample of 1001 adult Canadians who were representative of the entire adult population of Canada were interviewed by telephone for this survey. The results are considered accurate to within 3.1%, 19 times out of 20.
—© Copyright Ipsos Reid Public Affairs. Used with permission.
Read “Example 4: Analyzing statistical data to support a position” on page 300 of your textbook. Kylie used a number line to graph the overlap of the confidence intervals. As you read the example, think about what method you would use to show the overlap of the confidence intervals.
Self-Check 2
Complete “Practising” question 4 on page 302 of the textbook. Answer
This is the last lesson in this module. At this point, you may find it helpful to refer to the following items in Chapter 5 of your textbook and update your notes organizer at this time:
- “In Summary” boxes at the end of each section in the textbook
- “Mid-Chapter Review” on page 266 of the textbook
- “Chapter Review” on pages 306 and 307 of the textbook
It would be useful to review these concepts as you complete this module.