Business Smarts - Sample Module for Introduction to Statistics

1) A country uses street addresses to mail persons forms for a census. What is the target population?

 a)  The country's citizens.

 b)  The country's residents.

 c)  The persons in the country.

 d)  The country's home owners.

 e)  None of the above.

2) A country uses street addresses to mail persons forms for a census. What is the actual population?

 a)  The persons in the country living in homes, apartments, or hotels.

 b)  The persons in the country living in houses.

 c)  The persons in the country living in apartments.

 d)  The country's residents who are living someplace that receives mail.

 e)  None of the above.

3) A country uses street addresses to mail persons forms for a census. Does this method reach the entire target population identified in 1)?

 a)  Unqualified yes.

 b)  Unqualified no.

 c)  Qualified no.  Additional steps can be taken to reach those in shelters,
                      nursing homes, and hospitals.

 d)  Insufficient information.

 e)  None of the above.

4) A motor vehicle authority uses valid drivers' licenses to assess compliance with driver insurance regulations. What is the target population?

 a)  The residents in the jurisdiction.

 b)  The car drivers in the jurisdiction.

 c)  The holders of valid drivers' licenses in the jurisdiction.

 d)  The car owners in the jurisdiction.

 e)  None of the above.

5) A motor vehicle authority uses valid drivers' licenses to assess compliance with driver insurance regulations. What is the actual population?

 a)  The residents in the jurisdiction.

 b)  The car drivers in the jurisdiction.

 c)  The holders of valid drivers' licenses in the jurisdiction.

 d)  The car owners in the jurisdiction.

 e)  None of the above.

6) A motor vehicle authority uses valid drivers' licenses to assess compliance with driver insurance regulations. Does this method reach the entire target population identified in 3)?

 a)  Unqualified yes.

 b)  Unqualified no.

 c)  Qualified no.  Additional steps can be taken to reach car drivers who do not
                      hold valid drivers' licenses.

 d)  Insufficient information.

 e)  None of the above.

7) The taxing authority of a country uses federal identification numbers (FINs) of its citizens and permanent residents to select federal income tax returns for audits. A FIN is needed to earn and declare income. What is the target population?

 a)  Those in the country who are obliged to file income tax returns.

 b)  Those in the country who have a FIN, its citizens and permanent residents.

 c)  Those in the country who have income.

 d)  All of those in the country.

 e)  None of the above.

8) The taxing authority of a country uses federal identification numbers (FINs) to select federal income tax returns for audits. A FIN is needed to earn and declare income. What is the actual population?

 a)  Those in the country who are obliged to file income tax returns.

 b)  Those in the country who have a FIN, its citizens and permanent residents.

 c)  Those in the country who have income.

 d)  All of those in the country.

 e)  None of the above.

9) The taxing authority of a country uses federal identification numbers (FINs) to select federal income tax returns for audits. A FIN is needed to earn and declare income. Does this method reach the entire target population identified in 7)?

 a)  Unqualified yes.

 b)  Unqualified no.

 c)  Qualified no.  Additional steps can be taken to reach FIN holders who have
                      little income.

 d)  Insufficient information.

 e)  None of the above.

10) The taxing authority of a country uses federal identification numbers (FINs) to select federal income tax returns for audits. A FIN is needed to earn and declare income. Does this method reach the all those in whom the taxing authority might be interested?

 a)  Unqualified yes.

 b)  Unqualified no.

 c)  Qualified yes.  Additional steps can be taken to reach income earners who
                       do not have FINs.

 d)  Insufficient information.

 e)  None of the above.

Scenario I
A school district is planning for the upcoming school year wants to determine the average age of its primary school pupils from the school year just completed. It believes there are a total of 10,000 pupils in the district and wants to select 500 for a sample. The district analyst selects pupils from a list of those who achieved at least 75% attendence during the past school year.

11) The district analyst finds a sample mean age of 9 years and 3 months. Is this an unbiased estimate of the population mean age?

 a)  Unqualified yes.

 b)  Unqualified no.

 c)  Qualified no.  Additional steps can be taken to include pupils who plan
                      to attend school in the upcoming year.

 d)  Insufficient information.

 e)  None of the above.

12) If the sample mean is biased, what might be done to make the sample random and the sample mean unbiased?

 a)  Select pupils registered in the school district.

 b)  Select pupils with at least a 50% attendence record.

 c)  Select pupils only with a 100% attendence record.

 d)  Determine which pupils with less than 75% attendence are most likely to
       attend regularly in the upcoming year and include them in the sample.

 e)  None of the above.

13) A suggestion is made to select from all pupils who ever attended a district school. The analyst finds a sample mean of 9 years and 7 months. Is this an unbiased estimate if the mean age of actual population of pupils?

 a)  Unqualified yes.

 b)  Unqualified no.

 c)  Qualified no.  Additional steps can be taken to exclude pupils who
                      had very low attendence during the year.

 d)  Insufficient information.

 e)  None of the above.

14) What might best be done for the school district's selection method to make its actual population of pupils more closely match its target population of pupils?

 a)  Select from a list of pupils most likely to attend or enrol in
       school in the upcoming year.

 b)  Select from a list of pupils most likely to be registered in the
       school district in the upcoming year.

 c)  Select from a list of pupils who have committed to attend or enrol
       in school in the upcoming year.

 d)  None of the selection methods will make the actual population more
       closely match the target population.

 e)  None of the above.

Scenario II
A taxing authority is selecting tax returns to audit using a stratified sampling method. It samples 8 low income returns from a population of 2,000, and 12 high income returns from a population of 500. The income amounts sampled from the low income stratum are $10,200, $14,500, $16,000, $20,400, $12,800, $24,500, $18,900, $27,100. The income amounts from the high income stratum are $46,800, $52,200, $60,400, $48,700, $58,800, $77,800, $65,900, $73,600, $84,200, $80,800, $55,100, $67,300.

15) What is the raw weight for the low income sample values?

 a)  41.67.

 b)  0.004.

 c)  250.

 d)  0.024.

 e)  None of the above.

16) What is the adjusted weight for the high income sample values?

 a)  0.008.

 b)  2500.

 c)  2.0.

 d)  0.333.

 e)  None of the above.

17) What is the mean of the stratified sample?

 a)  $27,295.

 b)  $45,785.

 c)  $18,050.

 d)  $64,275.

 e)  None of the above.

Scenario III
An opinion polling firm is drawing a stratified sample for a client's survey. The population consists of 2,800 persons of European descent, 500 persons of African descent, and 700 persons of Hispanic descent. For the sample, it drew 28 European descendents, 10 African descendents, and 14 Hispanic descendents. The sampled person responded to the survey question with a number from 1 through 7, with 1 indicating full agreement and 7 indicating full disagreement. The European descendent opinions are: 1, 1, 3, 4, 2, 1, 2, 1, 3, 6, 2, 1, 3, 7, 5, 2, 1, 1, 2, 3, 1, 4, 7, 2, 2, 1, 1, 3. The African descendent opinions are: 3, 2, 3, 5, 4, 3, 4, 2, 3, 7. The Hispanic descendent opinions are: 3, 4, 3, 2, 5, 3, 7, 5, 6, 4, 3, 5, 3, 2.

18) What is the raw weight for the European descendent sample values?

 a)  0.02.

 b)  0.01.

 c)  50.

 d)  100.

 e)  None of the above.

19) What is the adjusted weight for the African descendent sample values?

 a)  0.65.

 b)  0.75.

 c)  0.25.

 d)  1.30.

 e)  None of the above.

20) What is the mean of the stratified sample?

 a)  3.13.

 b)  2.58.

 c)  2.74.

 d)  2.98.

 e)  None of the above.

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