a A sample is biased when it is not representative of the population. Are there any potentially popular sports that are not listed in the survey?
B
b The validity of a survey is considered to be the degree to which the results of the survey answer the question posed.
A
a See solution.
B
b No, see solution.
Practice makes perfect
a We are given information about a survey designed by a student. The survey is posted on a website and asks users to choose their favorite sport to play.
A sample is biased when it is not representative of the population. Let's think about how the design of this survey could introduce bias.
Reason
Potential Bias
Readers of the website choose to respond to the survey.
Since we cannot be sure that a sample is representative of the population, a self-selected sample is usually biased. For example, sports fans are more likely to respond to the survey.
The choice limits the options of respondents to only five sports.
There are a lot of popular sports that are not listed in the survey. For example, respondents might want to choose football, soccer, or martial arts as their favorite sport.
Only students are mentioned in the results.
We cannot be sure that only students will respond to the answer.
b We are asked if we believe that the results of the survey are valid. Let's take a look at the given circle graph.
Based on the reasons stated in Part A, we know that the design of the survey opens it up for bias. Therefore, the results of this survey are not valid.
Extra
Thinking About the Results
In addition to the bias that we already discussed, we can tell just by looking at the given results that something is probably off. rl
Basketball: & 35 %
Tennis: & 30 %
Golf: & 20 %
Swimming: & 10 %
Baseball: & 5 %
Does it seem reasonable that golf is the favorite sport of 20 % of students? Or that tennis is the second most popular? Many students cannot afford to play golf or tennis and many do not live anywhere near a golf course. Also, some of the most popular sports in the country — such as football and soccer — are not even listed. Even if we did not know anything about bias, we would have an idea that this survey was inaccurate.
