Education Technology

# Activities

• ##### Subject Area

• Math: Statistics: Sampling Distributions

9-12

45 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• ##### Software

TI-Nspire™ CX
TI-Nspire™ CX CAS

5.0

## Why t?

#### Activity Overview

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.

#### Objectives

• Students will recognize that when the population standard deviation is unknown, it must be estimated from the sample in order to calculate a standardized test statistic.
• Students will recognize that when the population standard deviation is known, the standardized test statistic for a sample mean (z-score) is unusual only when the sample mean itself is unusual (far from the population mean).
• Students will recognize that when the population standard deviation is unknown, the standardized test statistic for a sample mean (t-score) can be unusual for either of two reasons:
• because the sample mean itself is unusual (far from the population mean), or
• because the standard deviation of the sample (estimate of population sd) is small.
• Students will recognize that estimating the population standard deviation increases the variability of the sampling distribution of the standardized test statistic for sample means.

#### Vocabulary

• hypothesis test
• mean
• population
• sample
• sampling distribution
• standard deviation
• standardized test statistic
• t-score
• z-score