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# Random sampling | Lesson

## What are random samples?

A
without having to survey the entire group.
To make valid conclusions about a population, we need a sample that recreates the characteristics of the entire population on a smaller scale.
A good sample is representative and random.
• Representative means that the sample includes only members of the population being studied.
• Random means that every member of the population being studied has an equal chance to be selected for the sample.

### What skills are tested?

• Identifying a valid sampling method
• Determining the population for which the conclusions of a sample are valid
• Using a random sample to make an estimate

## What are some bad ways to sample?

Sampling method refers to how participants are selected for a sample.
Bad sampling methods include those that:
• Gather data from outside the population being studied
• Gather data that overrepresent or underrepresent a subgroup of the population (not random)

## What population can we make inferences about using data from a sample?

We can make inferences about only the population from which the random sample was selected.

## How can we use sample data to make an estimate?

We can use data from a random sample to estimate the number in the population having a particular attribute.
To make an estimate, we need to know the
and the population size.
$\text{estimate}=\text{population size}×\text{sample proportion}$

TRY: IDENTIFYING A VALID SAMPLING METHOD
A city manager wants to ask a sample of residents how they feel about different ways to mitigate traffic congestion. Which of the following methods of selecting the sample will yield the most valid information about the feelings of all residents of the city?

TRY: IDENTIFYING A VALID CONCLUSION
A veterinarian randomly tested $150$ of her canine patients for Lyme disease. $2\mathrm{%}$ of the canines tested positive for Lyme disease. Based on this data, which of the following conclusions are valid?

TRY: MAKING AN ESTIMATE
Jian asked a random sample of $700$ students at Golden University whether they have a microwave in their dorm room. Of the students surveyed, $210$ reported having a microwave in their dorm room. If there are $15,000$ students at Golden University, what is a reasonable estimate for the number of students who have a microwave in their dorm room?

TRY: MAKING AN ESTIMATE
$50$ randomly selected seniors at Lincoln High School were asked to state their intended college major. The bar graph above shows the results of the survey. If there are $600$ seniors at Lincoln High School, what is a reasonable estimate of the number of seniors who intend to major in business?

## Things to remember

A
is a way to gather information about a
without having to survey the entire group.
• A good sample must be both
and
!
We can use the results of a good sample to make estimates about the population it was drawn from.
• $\text{estimate}=$ $\text{population size}×\text{sample proportion}$
• Estimates are valid only for the specific population the sample is drawn from!

## Want to join the conversation?

• Is anyone else doing it backwards?
Instead of 600 multiplied by 6/50 = 72, I simplify the fraction and write it as 600 divided by 25/3 = 72. Same answer, different formula.
(1 vote)
• This is so confusing