Exercises

1. Do any of the following use simple random sampling? Provide a brief explanation of how each example uses this sampling method or not.
   1. bingo game Answer 1a
   2. Canadian election Answer 1b
   3. census Answer 1c
2. Imagine that a local clothing manufacturer has 2,700 employees. The personnel manager decides to ask the employees for suggestions on how to improve their workplace. It would take too long to survey everyone, so the manager chooses to systematically sample 300 of the employees.
   1. What would be the sampling interval? Answer 2a
   2. If the number 8 was your first randomly drawn number, what would be the first 5 numbers of your sample? Answer 2b
3. Suppose a national sports association wants to conduct a survey asking people living in Canadian capitals to choose their favourite team sport among hockey, lacrosse, curling and ringette.
   1. Copy the following table into your notebook. Fill in the missing province and capital information. (You can obtain the 2006 total population figures from Statistics Canada's Community Profiles website. In the 'Place name' space, type in the name of the capital city. Then, select a province or territory from the pull-down list. Hit the 'Search' button. When the available entries appear onscreen, choose the "city" – e.g. Regina (City). Do not use figures for census agglomerations or census metropolitan areas (CMAs).) Answer 3a
      
      

      Table 1.  Total population figures by capital cities in Canada, 2006

      Capital	Territory/Province	Total population 2006 Census
      	Yukon
      Yellowknife
      	Nunavut
      Victoria	British Columbia
      	Alberta
      Regina
      Winnipeg	Manitoba
      Toronto
      Québec
      	New Brunswick
      Halifax	Nova Scotia
      	Prince Edward Island
      St. John's	Newfoundland and Labrador

   2. What is the total population of all of the Canadian capital cities combined? Answer 3b
   3. Table 2 features the results of the fictional survey. Review this information and answer the following questions Answer 3c
      1. In what cities was hockey the most popular and the least popular?
      2. In what cities was lacrosse the most popular and the least popular?
      3. In what cities was curling the most popular and the least popular?
      4. In what cities was ringette the most popular and the least popular?

      Table 2.  Team sport preferences, selected capital cities, Canada

      	Victoria	Fredericton	Regina	Yellowknife	Toronto	Québec
      	%
      Hockey	10	3	58	23	71	29
      Lacrosse	46	11	25	5	7	11
      Curling	25	11	3	30	18	41
      Ringette	19	75	14	42	4	19
      Total	100	100	100	100	100	100

   4. If you were to break down the data into further categories, what would you suggest? Answer 3d
4. Poplar Ridge Academy has been given a sizeable grant: enough to build either a new library or gymnasium. But, as there is only money enough to build one facility, the principal wants to ask students which one they feel is in greater need of renovation.
   
   The table below indicates the number of students by sex, per grade, from Kindergarten to Grade 12.
   
   

   Table 3.  Number of students by sex and grade level, Poplar Ridge Academy

   	Kindergarten	1	2	3	4	5	6	7	8	9	10	11	12
   Boys	9	8	9	9	13	20	23	28	78	74	69	71	60
   Girls	6	8	11	10	13	18	35	34	63	62	61	88	70
   Total	15	16	20	19	26	38	58	62	141	136	130	159	130

   1. What is the total population of Poplar Ridge Academy? Answer 4a
   2. The principal wants to sample 50% of the students. How many students would this be? Answer 4b
   3. The principal wants to keep the correct proportion of girls to boys in the sample. Using the following formula, calculate the number of male Kindergarten students that should be included in the sample. Answer 4c
      
      
   4. What type of sampling technique has been used here? Answer 4d
   5. If the principal wishes to sample 180 students, how many boys and girls per grade should be surveyed? Put your answers in a table. (Results should be rounded to the nearest whole number.) Answer 4e

Class activities

1. Choose one of the random sampling methods described in this section to survey your class on each of the following topics:
   1. average number of children in a family
   2. type of transport used to get to school
   3. number of household pets, types (i.e., cat, dog, etc.) and breed.
2. Obtain the attendance registers for two classes given by your homeroom teacher that list the name and sex of each student. Using the stratified sampling technique, survey 20% of these classes to find out the overall favourite subjects for this group of students. Use sex and class as strata characteristics.