# Lesson 6Let’s InvestigateSolidify Understanding

## Learning Focus

Describe the difference between a survey, an experiment, and an observational study.

Design an investigation for a parameter of interest using appropriate study and sampling methods.

How can we determine if there is a cause-and-effect relationship between variables?

What features can we look for to help determine if study results are valid?

## Open Up the Math: Launch, Explore, Discuss

When we want to draw conclusions about some population, there are at least two different statistical ideas to consider. We learned about sampling in Would You Like to Try a Sample?, since it is usually more practical to sample the population rather than measure everyone or everything in the population.

The second thing to consider is how to measure the parameter of interest, the thing we want to know about the population. Sometimes it may not be too difficult to think of what and how to measure. For instance, if you want to know the average weight of a population, you might find a random sample of the population and then put each of the subjects on a scale. Three common techniques for designing studies are:

• Surveys: When they want to know how people feel, what their preferences are, what they own, how much they make, etc., researchers often construct a survey to ask the people in the sample about the parameter of interest.

• Observational Studies: In this type of study, researchers observe the behavior of the participants/subjects without trying to influence it in any way so they can learn about the parameter of interest.

• Experiments: In an experiment, researchers separate the participants into a control group and a treatment group, and manipulate the variables to try to determine cause and effect.

### 1.

Imagine that you want to know whether a new exercise routine improves fitness levels. You might choose any of the three methods to determine this.

• If you used a survey, you could ask people who had used the exercise routine if their fitness level changed.

• If you used an observational study, you might monitor volunteers who try the exercise routine and measure how much their fitness levels changed.

• If you used an experiment, you might randomly assign participants to two groups. One group (the control group) exercises as they normally would and the other group (the experimental group) exercises using only the new exercise routine. At the end of two months, the two groups are compared to see the average fitness change in each group.

Based on these three examples:

### 2.

Identify which method is illustrated by each example:

#### a.

To determine whether drinking orange juice prevents colds, researchers randomly assigned participants to a group that drank no orange juice or a group that drank two glasses of orange juice a day. They measured the number of colds that each group had over the course of the year and compared the results of the two groups.

#### b.

To determine whether exercise reduces the number of headaches, researchers randomly selected a group of participants and recorded the number of hours each participant exercised and the number of headaches each participant experienced.

#### d.

To determine if a new drug is an effective treatment for the flu, researchers randomly selected two groups of people who had the flu. One group was given a placebo (a sugar pill that has no physical effect) and one group was given the new drug. Researchers measured the number of days that participants experienced flu symptoms and compared the two groups to see if they were different.

#### e.

To determine if higher speed limits cause more traffic fatalities, researchers compared the number of traffic deaths on randomly selected stretches of highway with speed limits to the number of traffic deaths on an equal number of randomly selected stretches of highway with speed limits.

### 3.

Describe how you might select a sample and use a survey to investigate which soft drink people prefer: Fizzy Soda or Kooky Kola.

### 4.

Describe how you might select a sample and use an observational study to investigate which soft drink people prefer: Fizzy Soda or Kooky Kola.

### 5.

Describe how you might select a sample and use an experiment to investigate if consuming large quantities of Kooky Kola is associated with having headaches.

### 6.

Describe the method you would use to determine if excessive time on social media is associated with bad grades. Explain why you chose that method and what conclusions could be drawn from the study.

An experiment with a control group and a treatment group may be a study design that yields useful results. What factors in the design of the experiment might make it so that the results are not representative of the population?

Study Methods

Survey

Description:

Observation

Description:

Experiment

Description:

## Lesson Summary

In this lesson, we learned about three methods for investigating a research question. The methods are surveys, observational studies, and experiments. For the results of any of the investigations to be valid, researchers must use a random sampling method to select participants from the population.

## Retrieval

### 1.

Solve the system of equations.

### 2.

Recall the empirical rule is also referred to as the rule for a normally distributed variable.

The symbol for the mean is (mu) and the symbol for the standard deviation is (sigma).

• Approximately of the data lie within of the mean.

• Approximately of the data lie within of the mean.

• Approximately of the data lie within of the mean.

Fill in the numbers and important information for the rule on the sketch of the normal curve.