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Nineteen immigrants to the U.S were asked how many years, to the nearest year, they have lived in the U.S. The data are as follows:

  • 2
  • 5
  • 7
  • 2
  • 2
  • 10
  • 20
  • 15
  • 0
  • 7
  • 0
  • 20
  • 5
  • 12
  • 15
  • 12
  • 4
  • 5
  • 10

The following table was produced:

Frequency of immigrant survey responses
Data Frequency Relative Frequency Cumulative Relative Frequency
0 2 2 19 0.1053
2 3 3 19 0.2632
4 1 1 19 0.3158
5 3 3 19 0.1579
7 2 2 19 0.5789
10 2 2 19 0.6842
12 2 2 19 0.7895
15 1 1 19 0.8421
20 1 1 19 1.0000
  • Fix the errors on the table. Also, explain how someone might have arrived at the incorrect number(s).
  • Explain what is wrong with this statement: “47 percent of the people surveyed have lived in the U.S. for 5 years.”
  • Fix the statement above to make it correct.
  • What fraction of the people surveyed have lived in the U.S. 5 or 7 years?
  • What fraction of the people surveyed have lived in the U.S. at most 12 years?
  • What fraction of the people surveyed have lived in the U.S. fewer than 12 years?
  • What fraction of the people surveyed have lived in the U.S. from 5 to 20 years, inclusive?
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A “random survey” was conducted of 3274 people of the “microprocessor generation” (people born since 1971, the year the microprocessor was invented). It was reported that 48% of those individuals surveyed stated that if they had $2000 to spend, they would use it for computer equipment. Also, 66% of those surveyed considered themselves relatively savvy computer users. ( Source: San Jose Mercury News )

  • Do you consider the sample size large enough for a study of this type? Why or why not?
  • Based on your “gut feeling,” do you believe the percents accurately reflect the U.S. population for those individuals born since 1971? If not, do you think the percents of the population are actually higher or lower than the sample statistics? Why?

Additional information: The survey was reported by Intel Corporation of individuals who visited the Los Angeles Convention Center to see the Smithsonian Institure's road show called “America’s Smithsonian.”

  • With this additional information, do you feel that all demographic and ethnic groups were equally represented at the event? Why or why not?
  • With the additional information, comment on how accurately you think the sample statistics reflect the population parameters.
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  • List some practical difficulties involved in getting accurate results from a telephone survey.
  • List some practical difficulties involved in getting accurate results from a mailed survey.
  • With your classmates, brainstorm some ways to overcome these problems if you needed to conduct a phone or mail survey.
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Try these multiple choice questions

The next four questions refer to the following: A Lake Tahoe Community College instructor is interested in the mean number of days Lake Tahoe Community College math students are absent from class during a quarter.

What is the population she is interested in?

  • All Lake Tahoe Community College students
  • All Lake Tahoe Community College English students
  • All Lake Tahoe Community College students in her classes
  • All Lake Tahoe Community College math students

D

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Consider the following:

X = number of days a Lake Tahoe Community College math student is absent

In this case, X is an example of a:

  • Variable
  • Population
  • Statistic
  • Data

A

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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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