Exercises

1. Do any of the following use simple random sampling? Provide a brief explanation of how each example uses the sampling method.

a) bingo game
b) Canadian election
c) census

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.

a) What would be the sampling interval?
b) If the number 8 was your first randomly drawn number, what would be the first 5 numbers of your sample?

3. Suppose a national sports association wants to conduct a survey asking people living in Canadian capitals to choose their favourite of the following team sports: hockey, lacrosse, curling and ringette.

a) Copy the following table into your notebook. Fill in the missing province and capital information. (You can obtain the 2001 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, use only the figures for the cities, towns or regional municipalities. Do not use figures from the census agglomerations or census metropolitan areas (CMAs).)

**Table 1. Total population figures by capital cities in Canada, 2001**
Capital	Territory/Province	Total population 2001 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	-

b) What is the total population of all of the Canadian capital cities combined?
c) Table 2 features the results of the fictional survey. Review this information and answer the following questions:

i) Where was hockey the most popular and unpopular?
ii) Where was lacrosse the most popular and unpopular?
iii) Where was curling the most popular and unpopular?
iv) Where was ringette the most popular and unpopular?

**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

d) If you were to break down the data into further categories, what would you suggest?

e) How would you estimate the Canadian national team sport preferences, using the data for these cities?

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 her 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**
	K	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

K= Kindergarten

a) What is the total population of Poplar Ridge Academy?
b) The principal wants to sample 50% of the students. How many students would this be?
c) 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.

d) What type of sampling technique has been used here?
e) 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.)

Class activities

1. Choose one of the random sampling methods described in this section to survey your class on each of the following:

a) average number of children in a family
b) type of transport used to get to school
c) number of household pets, types (i.e., cat, dog, etc.) and breed.

2. Obtain the attendance registers for two homeroom classes that list both name and sex of each student. Using the stratified sampling technique, survey 20% of these classes to find out what the students' favourite subjects are. Use sex and homeroom classes as strata characteristics.

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