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Statistics, STD2 S1 2024 HSC 3 MC

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What type of sampling is this?

  1. Self-selecting
  2. Simple random
  3. Stratified
  4. Systematic
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\(A\)

Show Worked Solution

\(\text{By elimination}\)

\(\text{Option A: Individuals voluntarily choose to participate.}\ \checkmark\)

\(\text{Option B: Simple random sampling requires every individual in the population to have an equal chance of being selected.}\ \cross \)

\(\text{Options C and D: Both options refer to a systematic process for those included in the survey.}\ \cross \)

\(\Rightarrow A\)

Statistics, STD2 S1 2017 HSC 4 MC

A factory’s quality control department has tested every 50th item produced for possible defects.

What type of sampling has been used?

A.     Random

B.     Stratified

C.     Systematic

D.     Numerical

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`C`

Show Worked Solution

`text(A systematic sample divides a population)`

`text(into equal sample sizes and then selects)`

`text(equally among them.)`

`=> C`

Statistics, STD2 S1 2006 HSC 23c

Vicki wants to investigate the number of hours spent on homework by students at her high school.

  1. Briefly describe a valid method of randomly selecting 200 students for a sample.  (1 mark)

  2. Vicki chooses her sample and asks each student how many hours (to the nearest hour) they usually spend on homework during one week.

     

    The responses are shown in the frequency table.
     
         2UG-2006-23c

    What is the mean amount of time spent on homework?  (2 marks)

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  1. `text(A valid method would be using a stratified sample.)`

     

    `text(The number of students sampled in each year is)`

     

    `text(proportional to the size of each year.)`

  2. `text(7.275 hours)`
Show Worked Solution

i.   `text(A valid method would be using a stratified sample.)`

`text(The number of students sampled in each year is)`

`text(proportional to the size of each year.)`

MARKER’S COMMENT: This “routine” exercise of finding a mean from grouped data was incorrectly answered by most students! The best responses copied the table and inserted a class-centre column (see solution).

 

ii.    2UG-2006-23c Answer

 

`text(Mean)` `= text(Sum of Scores) / text(Total scores)`
  `= 1455/200`
  `= 7.275\ text(hours)`

Statistics, STD2 S1 2007 HSC 17 MC

Ms Wigginson decided to survey a sample of 10% of the students at her school.

The school enrolment is shown in the table. 
 


 

She surveyed the same number of students in each year group.

How would the numbers of students surveyed in Year 10 and Year 11 have changed if Ms Wigginson had chosen to use a stratified sample based on year groups? 

  1.    Increased in both Year 10 and Year 11
  2.    Decreased in both Year 10 and Year 11
  3.    Increased in Year 10 and decreased in Year 11
  4.    Decreased in Year 10 and increased in Year 11
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`C`

Show Worked Solution

`text(Total students surveyed)`

`= text(10%) xx 1200`

`= 120`

`text(Students surveyed per year group)`

`= 120/6`

`= 20`

 

`text(A stratified sample would have sampled 10%)`

`text(of each year group.)`

`text(In Year 10, 10%) xx 230 = 23`

`text(In Year 11, 10%) xx 150 = 15`

`:.\ text(More students sampled in Year 10 and)`

`text(less in Year 11.)`

`=>  C`

Statistics, STD2 S1 2011 HSC 25a

A study on the mobile phone usage of NSW high school students is to be conducted.

Data is to be gathered using a questionnaire.

The questionnaire begins with the three questions shown.

2UG 2011 25a

  1. Classify the type of data that will be collected in Q2 of the questionnaire.  (1 mark)

  2. Write a suitable question for this questionnaire that would provide discrete ordinal data.   (1 mark)

  3. An initial study is to be conducted using a stratified sample.

     

    Describe a method that could be used to obtain a representative stratified sample.  (1 mark)

  4. Who should be surveyed if it is decided to use a census for the study?  (1 mark)

Show Answers Only
  1. `text(Categorical)`
  2. `text(See Worked Solutions)`
  3. `text(See Worked Solutions)`
  4. `text(A census would involve all high school students in NSW.)`
Show Worked Solution

i.  `text(Categorical)`

 

ii.  `text(How many outgoing calls do you make per day?)`

`text{(Ensure it can be answered with a numerical score.)}`

 

iii.  `text(The method could be to work out how many)`

♦♦♦ Mean mark 7%. Toughest mark to get in the 2011 exam!
COMMENT: Know and be able to describe random, systematic and stratified sampling!

`text{students are in each year and ask 10% of the}`

`text{students in each year. (Note the sample of}`

`text{students in each year must be  proportional to}`

`text{their percentage in the population).}`

 

♦♦♦ Mean mark 18%.
MARKER’S COMMENT: A specific population needed (i.e. high school students).

iv.  `text(A census would involve all high school)`

`text(students in NSW.)`

Statistics, STD2 S1 2013 HSC 8 MC

A high school has 100 students in each year group, Year 7 to Year 12. A survey is to be conducted to determine the average number of text messages sent per month by students at the school.

Which of the following would provide the most representative sample for this survey?

  1. All Year 7 students
  2. All physics students in Year 11 and 12
  3. 20 students chosen at random from each year group
  4. 120 students chosen at random from the school roll
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`C`

Show Worked Solution

`text(The best sample would have an equal amount)`

`text(of people in each year randomly selected.)`

`=>\ C`