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### Course: Digital SAT Math>Unit 3

Lesson 10: Evaluating statistical claims: foundations

# Evaluating statistical claims | Lesson

A guide to evaluating statistical claims on the digital SAT

## What are evaluating statistical claims problems?

We routinely conduct research to answer questions such as "how many residents are in favor of a new law" or "is a new medical treatment effective?" While research results can give us powerful insights, we must carefully consider how the research is conducted, which in turn affects what conclusions can be drawn.
For example:
• If a survey was given to individuals of one ethnicity, then the results of the survey are not representative of individuals of other ethnicities.
• If a medical treatment is effective when tested on mice, we cannot conclude that the treatment is just as effective on humans without additional testing.
We won't be required to perform any calculations for these problems. Instead, we'll be asked to read fairly lengthy descriptions and then make logical observations or draw valid conclusions.
In this lesson, we'll learn to:
1. Recognize good and bad sampling methods
2. Draw valid conclusions from the results of surveys and experiments
You can learn anything. Let's do this!

## What are some good and bad sampling methods?

### Reasonable samples

Reasonable samplesSee video transcript

### Examples of bias in surveys

Examples of bias in surveysSee video transcript

### Example of "undercoverage" bias

Example of undercoverage introducing biasSee video transcript

### Sampling methods and their implications

Ideally, 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.
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)

### Try it!

try: identify flaws in sampling method
A school district employs $2,000$ teachers in its $40$ elementary, middle, and high schools. A high school teacher working for the district believes that teacher job satisfaction varies greatly from school to school and wants to estimate the proportion of all teachers in the district who are satisfied with their job.
Match each of the following sampling methods to the reason it's flawed.

## What are some different types of studies, and what conclusions can we draw from the results?

### Types of statistical studies

Types of statistical studiesSee video transcript

### Correlation and causality

Correlation and causalitySee video transcript

### Identifying study types

Worked example identifying experimentSee video transcript

### Drawing conclusions from study results

#### Sample surveys

We can draw conclusions about only the population from which the random sample was selected.

#### Controlled experiments

To understand the conclusions we can draw from controlled experiments, we must first understand the difference between correlation and causation.
• Correlation means there is a relationship or pattern between the values of two variables.
• Causation means that one event causes another event to occur.
You may have learned about controlled experiments and the scientific method in more detail in your science classes. For the SAT, the key takeaway is that a
is needed to establish a causal relationship.

### Try it!

try: extend sample results to a population
A youth activist group surveyed a random sample of $500$ teenagers between the ages of $16$ and $17$ in the U.S. to assess their opinions about lowering the voting age to $16$. The survey showed that the majority of those sampled were in favor of lowering the voting age to $16$. Based on the results, the majority of which of the following populations in the U.S. are most likely in favor of lowering the voting age to $16$ ?

try: determine whether a study establishes a causal relationship
An ice cream company randomly selected $100$ participants to test their new line of ice cream. For the study, each participant was given a pint of the new ice cream. The results showed that $98\mathrm{%}$ of the participants reported enhanced moods after consuming the ice cream.
Did the study have a control group?
Do the results of the study show that consuming the new ice cream is associated with reports of enhanced moods in the study participants?
Do the results of the study show that the new ice cream is more effective at enhancing the moods of people than other ice cream brands?

Practice: draw conclusion from sample data
A study was done on the lengths of frogs in a pond. A random sample of frogs were caught and tagged in order to ensure that none were measured more than once. The sample contained $50$ American bullfrogs, of which $40\mathrm{%}$ were shorter than $7$ inches. Which of the following conclusions is best supported by the sample data?

Practice: draw conclusion from research results
A study was conducted to determine if a new treatment is successful in treating
. $500$ participants were selected at random from a large population of people with insomnia. Half of the participants were randomly assigned to receive the treatment, and the other half did not receive the treatment. The resulting data showed that participants who received the treatment slept significantly better than those who did not. Based on the design and results of the study, which of the following in an appropriate conclusion?

## Want to join the conversation?

• Here i thought math just involved numbers and variables....
• No literally same
• I'm impressed by how Sal draws perfect circles effortlessly.
• Probably with a lot of practice. Even I'm amazed :D
• A Level/AP Psychology kids skipping through this fosho
• I'm homeschooled and I'm just skimming at this point lol.
• How often do questions like these come on the SAT?
• tbh I haven't encountered this type of question in the digital sat practice test. But, they were present in the pencil-paper test.
• And they say, math is numbers..... hmmm have a taste of this!
• Increasing the volume of video sounds would be the most helpful thing
• Wow. Reading comprehension has infiltrated the Math section
• Definitely biased towards people who already know how phonebooks work.
• it reminds me of my a levels psychology class (i dropped it after 3 months)
• same for me, this ones much easier though