# Statistics and Probability / Sample Proportions

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.