Review on Random Samples

Populations, Samples, and Generalizing from a Sample

Today, we will...

• learn about collecting data from a sample that is selected from a population

• what can be learned about the population by looking at a sample from that population

Multiple Choice

A ______ is the entire set of objects from which data might be collected

• sample

• population

• numerical summary

• statistic

Multiple Choice

A _______ is a subset of the population.

• population

• numerical value

• statistic

• sample

Multiple Choice

True or False: All samples lead to a good prediction about the entire population.

• True

• False

Multiple Choice

A student wants to know which type of of pizza high school students perfer. Which of the following options is a good, representative sample of the population?

• Asking all the 10th graders in the school

• Asking 20 students from each grade level

• Asking the school principal which type of pizza he perfers

• Asking the students who walk to school

Multiple Choice

A beverage company wants to see if people in the United States like their new logo. Which of the following represents the population?

• 2,000 people ages 5-13

• A selection of logo artists

• A selection of shoppers from different states

• all the people in the United States

Multiple Choice

A beverage company wants to see if people in the United States like their new logo. Which of the following represents the best choice for a sample?

• a collection of shoppers from different states

• all the people living in the United States

• a selection of logo artists

• 2,000 children from ages 5-13

Multiple Choice

Which of the following is NOT a reason why random samples are preferred over surveying the entire population.

• A random sample allows you to survey whoever you want.

• Surveying the entire population may cost too much money.

• Surveying the entire population takes too much time.

• Surveying the entire population can be a challenge because not everyone may respond.

Multiple Choice

Which of the following situations would you want to collect a sample rather than surveying the entire population?

• the median price of homes in Ohio

• how many students in the class like mushrooms on their pizza

• how many students have more than one pet

• the typical number of home runs for each player on the baseball team

Multiple Choice

A toy store owner wants to know how much kids spend each month on toys. Which choice is the best representation of the population?

• 220 wealthy kids

• all the kids who buy toys

• 100 boys ages 8-12

• 125 girls ages 10-15

Multiple Choice

Ana wants to know the average student’s opinion of the tardy policy at her school. Which group of students should she survey in order to achieve the most accurate results?

• 30 of her friends

• 30 randomly selected students in the school

• 30 students who are often tardy

• 30 students who are not often tardy

Multiple Choice

A survey company was trying to see if people in a state thought the pollution was too high. Which choice BEST represents the population to be surveyed?

• a selection of people who live in small towns

• a selection of people who live in clean neighborhoods

• a selection of people from each city in the state

• all the people in the state

Multiple Choice

A school principal wants to see which subject the 695 students in his school liked best. Which choice BEST represents a representative sample?

• all the girls in the school

• the students who have an A in math class

• the students who have a D in science class

• 1 classroom for each grade level

Multiple Choice

True or False: You want to see how many students take the bus home from school. You go to the bus stop and ask students how they get home everyday. This is a good, representation of the population.

• True

• False

Multiple Choice

Every possible group of units of the required size has the same chance of being the selected sample as any other sample of the same size.

• Simple Random 
• Thoughtful
• Typical
• Proportional

Multiple Choice

This sample is selected by dividing the population into subgroups and then taking a fixed number of units from each group using the simple random sample.

• stratified
• cluster
• judgment
• experimental

Multiple Choice

Cluster, stratified, simple random, systematic, and proportional are all types of 

• convenience samples
• biased samples
• haphazard samples
• unbiased samples

1-3 Data Collection and Sampling Techniques

You will be able to identify the four basic sampling techniques.

Four basic methods of sampling

• Random:  selected by using chance methods or random numbers. 

• Systematic: numbering each subject of the population and then selecting every kth subject. Chose a random 1st subject.

• Stratified: divide the population into groups (called strata) according to some characteristic that is important to the study, then sample from each group.

• Cluster Sampling: the population is divided into groups called clusters, then some of these clusters are randomly selected, and uses all members of the selected clusters as the subjects of the samples.

Simple Random Sampling Example

You want to select a simple random sample of 100 employees of Company X. You assign a number to every employee in the company database from 1 to 1000, and use a random number generator to select 100 numbers.

Systematic Sampling

All employees of the company are listed in alphabetical order. From the first 10 numbers, you randomly select a starting point: number 6. From number 6 onwards, every 10th person on the list is selected (6, 16, 26, 36, and so on), and you end up with a sample of 100 people.

Stratified Sampling

The company has 800 female employees and 200 male employees. You want to ensure that the sample reflects the gender balance of the company, so you sort the population into two strata based on gender. Then you use random sampling on each group, selecting 80 women and 20 men, which gives you a representative sample of 100 people.

Cluster Sampling

The company has offices in 10 cities across the country (all with roughly the same number of employees in similar roles). You don’t have the capacity to travel to every office to collect your data, so you use random sampling to select 3 offices – these are your clusters.

Multiple Choice

Mrs. Trahan samples her class by selecting 5 girls and 7 boys. This type of sampling is called?

• Stratified

• Systematic

• Simple

• Cluster

Multiple Choice

Farmer Joe separates his apple tree farm into 10 regions.  He counts the number of apples produced in just one of the regions and uses that estimate to predict the number of apples produced on the whole farm.  This is _______ sampling.

• Simple
• Cluster
• Stratified
• Systematic

Multiple Choice

Mrs. Trahan samples her class by picking 10 numbers from her hat and each number is assigned to a student. This is ______________ random sampling.

• Systematic
• Simple
• Stratified
• Cluster

Multiple Choice

Mrs. Trahan samples her class by selecting all students sitting at group 1 and group 5 in her classroom.  This sampling technique is called?

• Simple
• Stratified
• Systematic
• Cluster

Multiple Choice

Farmer Joe randomly picks 100 trees using a random number generator to estimate the number of apples produced by his apple trees. This is ______________ sampling.

• Simple

• Stratified

• Cluster

• Systematic

Multiple Choice

Mrs. Trahan samples her class by selecting 5 girls and 7 boys. This type of sampling is called?

• Stratified

• Systematic

• Simple

• Cluster

Multiple Choice

Farmer Joe's apple tree farm is set up in 100 rows. He counts the number of apples produced on every 10th row to estimate the number apples produced on the whole farm. This is _____________ sampling.

• Simple

• Stratified

• Cluster

• Systematic

Multiple Choice

A group of people were asked about their favorite types of pants. Predict how many people out of 150 would say jeans are their favorite.

• 150

• 50

• 25

• 75

Multiple Choice

A group was surveyed and asked about their favorite sport.  Predict how many people would chose football if there are 600 students in the school.

• 150

• 180

• 450

• 600

Multiple Choice

You did a survey and found out 65% of people like mustard on their hot dog. If there are 2,500 residents of a town, predict how many would say they like mustard on their hot dog.

• 65

• 1,625

• 2,000

• 2,500

Multiple Choice

Allie wants to learn the most popular board game in the United States, so she creates a poll and shares it on Twitter. Random or Biased/

• Random

• Biased

Multiple Choice

Zeke wants to find out how 7th graders at OMS get to school so he places the names of all 7th graders into a fish bowl and pulls out 50 names so he can survey them. Random or Biased?

• Random

• Biased

Multiple Choice

Jacob wants to determine the favorite candy among all 7th graders. He asks all the people who sit in his row in Math class. Random or Biased?

• Random

• Biased

Multiple Choice

A town has 35,000 registered voters. A random sample of 500 voters finds that 125 are in favor of a new dog park. How many voters are likely to vote for the dog park?

• 8,750

• 2,625

• 125

• 2,500