Download Introduction to Chance Models (Section 1.1) Introduction A key step

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7. Do you think the words you selected are representative of the 268 words in this
passage? Suggest a method for deciding whether you have a representative sample.
(Hint: Whereas any one sample may not produce statistics that exactly equal the
population parameters, what would we like to be true in general?)
8. Combine your results with your classmates’ by producing a dotplot of the distribution of
average word lengths in your samples. Be sure to label the axis of this dotplot
appropriately. Describe the shape, center, and variability of the distribution of average
word lengths as revealed in the dotplot.
9. Let’s compare your sample statistics to the population parameter. How many and what
proportion of students in your class obtained a sample average word lengths larger than
4.29 letters, the average word length in the population?
Definition: A sampling method is biased if, when using that sampling method, statistics from
different samples consistently overestimate or consistently underestimate the population
parameter of interest.
Note that bias is a property of a sampling method, not a property of an individual sample. Also
note that the sampling method must consistently produce non-representative results in order to
be considered biased.
10. What does your answer to #9 tell you about whether the sampling method of asking
students to quickly pick 10 representative words is biased or unbiased? If biased, what is
the direction of the bias (tendency to overestimate or to underestimate)?
11. Do you think asking each of you to take 20 words instead of 10 words have helped with
this issue? Explain.
June 27, 2014
MAA PREP workshop
50