## Vacation in the Bahamas

## Opening

# Vacation in the Bahamas

Estimate the probability that a person from the United States chosen at random will vacation in the Bahamas this summer.

- How would you go about finding this probability?

Estimate the probability that a person from the United States chosen at random will vacation in the Bahamas this summer.

- How would you go about finding this probability?

Discuss the following with your classmates.

- A
*sample*is part of a larger group of objects or people. The larger group is called a*population*. - A population can be any group that is appropriate for a particular situation. For example, a population might be defined as the 5,500 residents of a certain city, or the whole population of the United States. In a factory, the population might be the number of items produced in any one day, or the number of items produced in a year.
- A sample must be selected randomly from the population so as to ensure that there is no bias toward one sector of the population or toward any particular result. In a random sample, every member of a population is equally likely to be selected.

Identify samples and populations, and understand how to choose a random sample from a population.

Sample size and population size go together. If the population is not too large, the sample size could be the whole population.

What population might these samples have been taken from?

- Two thousand residents of voting age in a particular city are surveyed about their voting intentions.
- Students in a seventh grade class are surveyed about their favorite music group.
- Scientists catch and tag 10 fish in a lake.
- One hundred of the lightbulbs produced in a factory in one day are surveyed for flaws.

For each situation, decide whether it would be better to survey the population or a sample.

- The shoe sizes of 12 students
- The ages of people who watch professional basketball on television
- The scores that students in your class receive on a math test

The makers of Juicy Orange Juice are proud their juice is sold in supermarkets across ten states.

They want to conduct a survey to determine customer satisfaction with their product.

- Describe the target population of the survey.
- It is more practical for the Juicy Orange Juice Company to survey a sample rather than the population? Explain why.

A company executive suggests printing an invitation on the bottle label asking people to phone the Juicy Orange Juice Company with their opinions of the product.

- Describe what is wrong with the sampling method.
- How would you recommend they determine the sample for the survey?
- Would the population be the whole United States?
- How many people do you estimate would be in the population? Would it make sense to survey all of them?
- What type of people might phone in? Would they be different from other members of the population?

Explain the difference between a sample and a population, and how to choose a random sample from a population. Use your work to illustrate your explanations.

- How would you choose a sample to predict which candidate people will vote for in the next presidential election?

Take notes about students' explanations for samples and populations.

As your classmates present, ask questions such as:

- How does the size of the population affect the size of the sample needed?
- What makes a sample biased?
- What method did you propose to the Juicy Orange Juice Company? Why is your method a good one?
- What types of factors do you need to consider when selecting a random sample?
- Can you think of another example of a population and a random sample for that population?

**Read and Discuss**

Samples that are not chosen using a random method are likely to be biased toward a certain outcome because they do not represent the population. Here are some examples of non-random sampling:

**Convenience sampling:**People who are readily available are chosen, such as people entering a shopping mall being asked if they like shopping**Self-selected sampling:**People are asked to call in or fill out a questionnaire to give their opinion; people who respond are likely to have strong opinions**Systematic sampling:**People are selected according to a system, such as choosing every third person on a list; each person is not equally likely to be chosen

Can you:

- Define
*sample*and*population*? - Explain what makes a good sample?

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**An example of biased data is…**