## Statistics

### Sampling Distributions

The distribution of a statistic calculated from all possible samples of the same size drawn from a population is known as a sampling distribution for that statistic. In these lessons, students investigate the mean and standard deviation of sampling distributions of sample means and related concepts such as why the sample standard deviation is calculated by dividing by n-1 and the n < 10%N rule. Students will simulate sampling distributions and investigate the difference between a t and a z distribution.

### Statistics: Sampling Distributions Activities

Title Type

#### Why t?

This lesson involves examining the variability of individual elements and their related standardized test statistics when those elements are drawn randomly from a given normally-distributed population.

• 3103

#### 10% Rule

This lesson involves investigating the differences between the standard deviations of sampling distributions of means for samples taken from finite populations with and without replacement.

• 3369

#### Family of t Curves

This lesson involves investigating how a t-distribution compares to a normal distribution.

• 3063

#### German Tanks: Exploring Sampling Distributions

In this lesson, students will estimate the largest number of a population based on random samples from the population, as statisticians did in WWII.

• 3116

#### Sampling Distributions

This lesson involves examining samples from a normal population and observing the distribution of the means of those samples.

• 4474

#### Why Divide by n-1?

Students will investigate calculating a sample variance using both n and n-1 as the divisor for samples drawn with and without replacement.

• 4453

#### Central Limit Theorem

This lesson involves examining distributions of sample means of random samples of size n from four different populations.

• 3305

#### Standard Error and Sampling Means

This lesson involves investigating the relationship between the standard deviation of a population, the area of a set of rectangles, and the standard deviation of the sampling distribution of sample mean areas of the rectangles.

• 3097