Download IRA Guide for Section 8.1

Interactive Reading Assignment Guide
Section 8.1
Introduction
Screen 1: This is a review problem on the different sampling techniques (systematic, convenience,
cluster, stratified, simple random. Go back to section 1.3 if you need a refresher.
Screen 2: This problem focuses on determining the population and/or the sample mean from a data
set. Go back to section 3.1 if you need a refresher.
Screen 3: This problem focuses on determining the population and/or the sample standard deviation
from a data set. Go back to section 3.2 if you need a refresher.
Screen 4: This problem focuses on calculating probabilities using the normal probability calculator. Go
back to section 7.1 & 7.2 if you need a refresher.
Screen 5: List of Objectives. Also a brief statement about how we can approximate the population
mean using different sampling techniques and referencing the “sampling distribution.”
Screen 6: The screen shows the definitions of a sampling distribution.
Objective 1: Describe the Distribution of the Sample Mean: Normal Population
Screen 1: The video on this screen demonstrates how we can find a “sampling distribution” using a
computer simulation. The sampling distribution is the distribution that is created by taking
multiple samples from the same population.
Screen 2: This screen demonstrates how to find the mean and standard deviation of a sampling
distribution. Here is what you need to know:
̅’s (sample means) is the same as
1. The mean of the sampling distributions for all of the 𝒙
the mean of the population.
𝝁𝒙̅ = 𝝁
̅’s (sample means) is the
2. The standard deviation of the sampling distribution for all of the 𝒙
sample as the standard deviation of the population divided by the square root of n.
𝝈𝒙̅ =
𝝈
√𝒏
Screen 3: This screen shows how to use the formulas (above) to approximate the mean and
standard deviation of a sampling distribution.
Screen 4: This screen states that the shape of the sampling distribution of 𝑥̅ is normal, if the
population is normal.
Developed by Sharleen McCarroll in conjunction with the textbook Interactive Statistics: Informed Decisions Using Data, by
Michael Sullivan III & George Woodbury, 2016.
Screen 5: This activity allows you to simulate taking multiple samples from a population that has a
normal distribution.
Screen 6: This question asks you information about the sampling distribution for 𝑥̅ . This information
was covered on the previous screens. You only get ONE attempt on this problem.
Screen 7: Example 1. This example demonstrates how to find the probabilities for a sampling
distribution. Watch the STAT CRUNCH video.
Screen 8: This problem is like the problem in example 1. Be sure to use Stat Crunch.
Objective 2: Describe the Distribution of the Sample Mean: Non-Normal Populations.
Screen 1: The video on this screen demonstrates how we can find a “sampling distribution” from a
non-normal population using a computer simulation. The sampling distribution is the distribution
that is created by taking multiple samples from the same population.
Screen 2: On this screen you will find the Central Limit Theorem, which is an important Theorem in
Statistics. Watch the “In Other Word” video.
Scree 3: This screen describes how large your sample size should be in order to assume that the
distribution for 𝑥̅ to be normal. As a general rule, we will use a sample size of 30 or greater to be
enough in order to assume that 𝑥̅ has a normal distribution. (In practice, your sample size may have
to be larger than 30, but we will use 𝑛 ≥ 30 for the rest of this class.)
Screen 4: On this screen, you will find an illustration of a population with three different samples
taken from the same population. You should notice that as n gets larger, the sampling distribution
starts to look more like the symmetric or bell-shape.
Screen 5: General rule of thumb for using the Central Limit Theorem. (You should try to remember
these rules.)
Screen 6: Activity 1. This activity will allow you the opportunity to generate many different sample
from a population. You can see the population distribution, the sample distribution (for 1 sample),
and the sampling distribution of sample means (the distribution for all of the 𝑥̅ ’s).
Screen 7: This question is based off your conclusions from the activity. Be careful – you only get
one chance on this question.
Screen 8: Example 2. This example demonstrates how to calculate probabilities and z-scores for
sample means. You should watch the “by hand” so you understand the process and the Stat Crunch
video solutions.
Screen 9: This problem is like the problem on the previous screen.
Screen 10: This is a great summary video. Be sure to watch this video.
Screen 11: End of Section.