# Statistics and Probability / Sample Proportions

Grade Level 7,8
Activity 19 of 24
In this lesson, students investigate the effect of sample size on variability by comparing the distribution of sample proportions with the population proportion.

## Planning and Resources

Objectives
Students understand sampling variability as the variation from sample to sample in the values of a sample statistic. They understand that the sampling variability among samples is related to size of the samples; as the sample size increases, the variability decreases.

Vocabulary
random sample
sampling variability
sampling distributions of a statistic (the proportion)
simulated sampling distributions

Standard:

## Lesson Snapshot

#### Understanding

A sampling distribution is the collection of sample statistics from all possible samples of a given size from a population.

### What to look for

When comparing simulated sampling distributions, be sure the sample size is the same unless the file has been set to proportions rather than counts.

### Sample Assessment

Would you rather go to a small hospital where a sample of 10 operations showed that 8 of them were successful or to a large hospital where on average 75% of the operations are successful? Give a reason for your answer.

Response:
The large one because a small sample can have a lot of variability and it did not say it was random. When something happens “On average” there will be some variability but the variability will be close to the 75%.

#### The Big Idea

A statistic computed from a random sample can be used as an estimate of that same characteristic of the population from which the sample was selected.

### What are the students doing?

Students investigate the relationship between sample size and the shape of simulated distribution of the proportion of successes in random samples.

### What is the teacher doing?

Be sure students recognize that sample proportions cluster around the population proportion. The distributions of the sample statistic for a given sample size have a fairly predictable shape and spread.