7.04 Sampling techniques
Hannah has chosen to collect information using a sample instead of a census.
State the advantages of a sample.
Peter has chosen to collect information using a census instead of a sample.
State the advantages of a census.
Determine whether the following is a census or sample:
Lucy has asked everyone in her office what snacks should be provided in the office.
James asks a few of his friends how they did in the test to see if he is above average in his class.
Joanne finds the height of the entire class to try to find the average height of 15-year old students in America.
Justin has determined the age of 10\% of houses from each suburb in Delaware.
Valentina tests every engine that the factory produces.
Oprah checks every dog brought to her vet to assess the treatment of dogs in the city.
Asking all the teachers at your school whether they approve of a new class timetable.
A taste test of a large batch of cookies Michael just baked.
Determine whether a census or sample would be better for the following examples, and explain your choice:
A school teacher wants to find out what grade level his students are reading at.
A college student wants to find the average reaction times for people.
A hospital wants to find out which heart rate machines are faulty.
A store manager wants to know the exact number of stolen items from the store.
A farmer wants to find the average height of the stalks of wheat in his field.
Tricia wants to make sure the fireworks that she creates explode properly.
The local mayor wants to determine how people in her town feel about the new construction project. State the type of sampling that each of the following scenarios use:
Selecting every 50th name from an alphabetical list of residents.
Giving each resident a random number between 1 and 10 and then selecting everyone with the number 3.
Selecting 10\% of the residents from each suburb.
At a music concert, there is expected to be a crowd of 3240 people. The band is giving away some shirts for some people that attend based on what order they enter the venue.
If the band are to give away 18 shirts, find the proportion of people that will get shirts.
If the band are to give away 60 shirts, find the proportion of people that will get shirts.
In a group of 360 students, 90 are elementary students and 270 are high school students. A stratified sample of 120 is to be selected from the group based on grade level.
How many elementary students should be selected?
How many high school students should be selected?
Users of a particular streaming service can be in one of four categories: Standard, Family, Premium, or Business. The table shows the number of people in each category:
How many customers are there across all the categories?
If a stratified sample of 400 is to be taken from the group, state the proportion of people who will be chosen.
For the sample to be stratified, give the number of customers that should be chosen in each category:
Standard
Family
Premium
Business
| Team | Number of people |
|---|---|
| \text{Standard} | 3500 |
| \text{Family} | 1500 |
| \text{Premium} | 2000 |
| \text{Business} | 3000 |
The owner of a movie theater wants to use stratified sampling in their survey of people who come to their movie theater.
Determine whether the methods below would be considered as stratified sampling:
Interview 10\% of the people who used the candy bar and 10\% of people who didn't.
Interview every person that sees a romantic movie.
Interview 10\% of the people from each movie.
Interview every 10th person that purchases a ticket.
A factory produces 1820 TVs every day. Find the number of TVs that are tested daily if the factory tests a systematic sample of:
Every 13th TV.
Every 70th TV.
The principal wants to use systematic sampling in their survey on how students in their school feel about the new auditorium.
Determine whether they can use the following systematic sampling methods:
Interview every 7th person on the school student list for that grade.
Interview every 7th person that walks past their office.
Interview one random person from each class in that grade.
Organize every student in the grade by their height and then select every 7th person in the line.
Interview 110 random people from the grade.
Beth is interested in which students from her school catch public transport.
Determine whether or not the following sampling methods are likely to be biased:
Selecting every 10th person on the bus she catches.
Selecting every 10th person on the student list.
Selecting the first 50 students that arrive in the morning.
Selecting by having a computer randomly choose student numbers.
Georgia wants to know how the people in America are going to vote in an upcoming election. She selects 50 random people from her city to interview.
Suggest reasons why this sampling might give poor results.
Justin wants to know how the students at his school might vote for the next class president. He leaves three flyers in each classroom to complete by whatever students want to complete them.
Suggest reasons why this sampling might give poor results.