NZ Level 7 (NZC) Level 2 (NCEA) Sampling Techniques

## Interactive practice questions

Prior to an election, a news editor wanted to view the opinions of randomly selected people. Some two digit numbers were randomly generated, as shown in the picture, and starting with $37$37, the editor would choose a number $3$3 to the right, $1$1 down (so that the next number chosen would be $57$57). The numbers chosen were the ages of the people she would survey.

 $37$37 $49$49 $19$19 $72$72 $38$38 $33$33 $80$80 $83$83 $90$90 $23$23 $78$78 $21$21 $29$29 $72$72 $40$40 $85$85 $79$79 $84$84 $57$57 $46$46 $49$49 $53$53 $55$55 $51$51 $36$36 $66$66 $61$61 $86$86 $66$66 $41$41 $74$74 $71$71 $40$40 $49$49 $42$42 $17$17 $50$50 $68$68 $27$27 $15$15 $47$47 $70$70 $47$47 $63$63 $32$32 $37$37 $33$33 $84$84 $34$34 $35$35 $51$51 $50$50 $87$87 $65$65 $47$47 $38$38 $78$78 $80$80 $39$39 $60$60 $23$23 $82$82 $64$64 $22$22 $21$21 $76$76 $38$38 $67$67 $43$43 $75$75 $39$39 $76$76 $72$72 $48$48 $33$33
a

What are all the random numbers the editor chose?

b

What is the range in ages of the people who will be surveyed?

Easy
Approx 4 minutes

In a study of asthma sufferers, a group of people are asked to identify which category they fit into:

• A - developed asthma from ages $0$0 to $10$10
• B - developed asthma in their teens
• C - developed asthma in their twenties
• D - developed asthma after the age of $30$30

Researchers then generated random values between $0$0 and $1$1 to decide which groups to choose participants from.

A manager wants to randomly select products on an assembly line to test their quality. She generates a random number between $2$2 and $10$10, which tells her how many products to pass before picking up the next one. She then generates another random number and so on.

The first product she picks up is the first one on the assembly line.

She then generates the following numbers:

$10$10 $11$11 $7$7 $14$14 $4$4

The following table shows the gender of $50$50 Year 12 students at a particular school.

 Students $1$1-$10$10 $\text{m },\text{f },\text{m },\text{f },\text{ f },\text{m },\text{m },\text{m },\text{f },\text{m }$m ,f ,m ,f , f ,m ,m ,m ,f ,m Students $11$11-$20$20 $\text{m },\text{f },\text{m },\text{m },\text{f },\text{m },\text{f },\text{m },\text{f },\text{f }$m ,f ,m ,m ,f ,m ,f ,m ,f ,f Students $21$21-$30$30 $\text{f },\text{ f },\text{m },\text{m },\text{f },\text{m },\text{m },\text{f },\text{f },\text{f }$f , f ,m ,m ,f ,m ,m ,f ,f ,f Students $31$31-$40$40 $\text{m },\text{f },\text{m },\text{f },\text{f },\text{f },\text{m },\text{m },\text{m },\text{f }$m ,f ,m ,f ,f ,f ,m ,m ,m ,f Students $41$41-$50$50 $\text{f },\text{m },\text{f },\text{m },\text{m },\text{ f },\text{m },\text{f },\text{m },\text{f }$f ,m ,f ,m ,m , f ,m ,f ,m ,f

### Outcomes

#### S7-1

Carry out investigations of phenomena, using the statistical enquiry cycle: A conducting surveys that require random sampling techniques, conducting experiments, and using existing data sets B evaluating the choice of measures for variables and the sampling and data collection methods used C using relevant contextual knowledge, exploratory data analysis, and statistical inference.

#### 91263

Design a questionnaire