When you are working with nominal proportional data,

Sample to Sample or Sample to Population for Z-tests of Proportions

When you are working with nominal proportional data, you need to determine if you are being asked to compare a sample to another sample

Sample to Sample or Sample to Population for Z-tests of Proportions

When you are working with nominal proportional data, you need to determine if you are being asked to compare a sample to another sample or a sample to a population or a claim.

Sample to Sample or Sample to Population for Z-tests of Proportions

Here are your options:

Sample to Sample or Sample to Population for Z-tests of Proportions

Here are your options:

Sample to Sample

Sample to Population

Sample to Sample or Sample to Population for Z-tests of Proportions

Let’s look at a few examples to distinguish sample to sample from sample to population comparisons.

Sample to Sample or Sample to Population for Z-tests of Proportions

Sample to Population

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% (9 out of 10) customers are very satisfied with a particular vacuum brand.

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% (9 out of 10) customers are very satisfied with a particular vacuum brand.

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% (9 out of 10) customers are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product.

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% (9 out of 10) customers are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% (9 out of 10) customers are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% (9 out of 10) customers are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

First of all, we know that we are dealing with nominal proportional data because there is a

percentage (90%) or a proportion (9 out of 10 / 15 out of 20).

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% (9 out of 10) customers are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

First of all, we know that we are dealing with nominal proportional data because there is a

percentage (90%) or a proportion (9 out of 10 / 15 out of 20).

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% (r 9 out of 10) customers are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

First of all, we know that we are dealing with nominal proportional data because there is a

percentage (90%) or a proportion (9 out of 10 / 15 out of 20).

Percentage

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% (9 out of 10) customers are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

First of all, we know that we are dealing with nominal proportional data because there is a

percentage (90%) or a proportion (9 out of 10 / 15 out of 20).

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% (9 out of 10) customers are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

First of all, we know that we are dealing with nominal proportional data because there is a

percentage (90%) or a proportion (9 out of 10 / 15 out of 20).

Proportion

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% (or 9 out of 10) customers are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

First of all, we know that we are dealing with nominal proportional data because there is a

percentage (90%) or a proportion (9 out of 10 / 15 out of 20).

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% (or 9 out of 10) customers are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

First of all, we know that we are dealing with nominal proportional data because there is a

percentage (90%) or a proportion (9 out of 10 / 15 out of 20).

Proportion

Sample to Sample or Sample to Population for Z-tests of Proportions

So, now we know that we are dealing with nominal proportional data.

Sample to Sample or Sample to Population for Z-tests of Proportions

So, now we know that we are dealing with nominal proportional data.

In this case the nominal data consists of 1s and 2s.

1 = very satisfied with the vacuum2 = not very satisfied with the vacuum

Sample to Sample or Sample to Population for Z-tests of Proportions

So, now we know that we are dealing with nominal proportional data.

In this case the nominal data consists of 1s and 2s.

1 = very satisfied with the vacuum2 = not very satisfied with the vacuum

Sample to Sample or Sample to Population for Z-tests of Proportions

So, now we know that we are dealing with nominal proportional data.

Sample to Sample or Sample to Population for Z-tests of Proportions

So, now we know that we are dealing with nominal proportional data.

The nominal data is proportional because it is reported as a proportion or a percentage:

Percentage = 90%Proportion = 9 out of 10

Sample to Sample or Sample to Population for Z-tests of Proportions

So, now we know that we are dealing with nominal proportional data.

The nominal data is proportional because it is reported as a proportion or a percentage:

Percentage = 90%Proportion = 9 out of 10

Sample to Sample or Sample to Population for Z-tests of Proportions

So, now we know that we are dealing with nominal proportional data.

Or

Percentage = 75%Proportion = 15 out of 20

Sample to Sample or Sample to Population for Z-tests of Proportions

Then, we determine if this is a sample to sample or sample to population question.

Sample to Sample or Sample to Population for Z-tests of Proportions

Here is the problem again:

Sample to Sample or Sample to Population for Z-tests of Proportions

Here is the problem again:

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% of all customers (9 out of 10) are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

Sample to Sample or Sample to Population for Z-tests of Proportions

A population is a defined group where all the members are accounted for in terms of some outcome.

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% of all customers (9 out of 10) are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

Sample to Sample or Sample to Population for Z-tests of Proportions

In this case the defined group is all customers

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% of all customers (9 out of 10) are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

Sample to Sample or Sample to Population for Z-tests of Proportions

The outcome is vacuum satisfaction

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% of all customers (9 out of 10) are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

Sample to Sample or Sample to Population for Z-tests of Proportions

The outcome is vacuum satisfaction

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% of all customers (9 out of 10) are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

Sample to Sample or Sample to Population for Z-tests of Proportions

Since it states all customers, then we assume we are talking about a population.

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% of all customers (9 out of 10) are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

Sample to Sample or Sample to Population for Z-tests of Proportions

In most cases it will not state “all customers” but a population is implied by the claim “9 out of 10 are very satisfied”.

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% of all customers (9 out of 10) are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

Sample to Sample or Sample to Population for Z-tests of Proportions

So, we are comparing this population

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% of all customers (9 out of 10) are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% of all customers (9 out of 10) are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

So, we are comparing this population with this sample.

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% of all customers (9 out of 10) are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

So, we are comparing this population with this sample.

Sample to Sample or Sample to Population for Z-tests of Proportions

So, we are comparing this population with this sample.

You have been asked by your marketing team leader to determine if a claim by an infomercial is true. They claim that 90% of all customers (9 out of 10) are very satisfied with a particular vacuum brand.

You select a sample of 20 of these vacuum brand owners and ask them if they are very satisfied with the product. Fifteen respond that they are very satisfied and five respond that they are not.

Is their claim statistically significantly accurate or not?

This is an example of a Sample to Population problem

Sample to Sample or Sample to Population for Z-tests of Proportions

Sample to Sample

Sample to Population

Sample to Sample or Sample to Population for Z-tests of Proportions

What does a sample to sample problem look like?

Sample to Sample or Sample to Population for Z-tests of Proportions

Let’s look at the same example with some slight changes to it.

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a sample of owners of vacuum brand “X” have statistically different satisfaction results (80% or 8 out of 10 satisfied) with a sample of owners who use vacuum brand “Y” (75% or 7.5 out of 10).

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a sample of owners of vacuum brand “X” have statistically different satisfaction results (80% or 8 out of 10 satisfied) with a sample of owners who use vacuum brand “Y” (75% or 7.5 out of 10).

First, we know that we are dealing with nominal proportional data.

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a sample of owners of vacuum brand “X” have statistically different satisfaction results (80% or 8 out of 10 satisfied) with a sample of owners who use vacuum brand “Y” (75% or 7.5 out of 10).

First, we know that we are dealing with nominal proportional data.

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a sample of owners of vacuum brand “X” have statistically different satisfaction results (80% or 8 out of 10 satisfied) with a sample of owners who use vacuum brand “Y” (75% or 7.5 out of 10).

Second, we are comparing two samples.

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a sample of owners of vacuum brand “X” have statistically different satisfaction results (80% or 8 out of 10 satisfied) with a sample of owners who use vacuum brand “Y” (75% or 7.5 out of 10).

Second, we are comparing two samples.

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a sample of owners of vacuum brand “X” have statistically different satisfaction results (80% or 8 out of 10 satisfied) with a sample of owners who use vacuum brand “Y” (75% or 7.5 out of 10).

Second, we are comparing two samples.

1st Sample

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a sample of owners of vacuum brand “X” have statistically different satisfaction results (80% or 8 out of 10 satisfied) with a sample of owners who use vacuum brand “Y” (75% or 7.5 out of 10).

Second, we are comparing two samples.

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a sample of owners of vacuum brand “X” have statistically different satisfaction results (80% or 8 out of 10 satisfied) with a sample of owners who use vacuum brand “Y” (75% or 7.5 out of 10).

Second, we are comparing two samples.

2nd Sample

Sample to Sample or Sample to Population for Z-tests of Proportions

You have been asked by your marketing team leader to determine if a sample of owners of vacuum brand “X” have statistically different satisfaction results (80% or 8 out of 10 satisfied) with a sample of owners who use vacuum brand “Y” (75% or 7.5 out of 10).

2nd SampleThis is an example of a

Sample to Sample problem

Sample to Sample or Sample to Population for Z-tests of Proportions

Sample to Sample

Sample to Population

Sample to Sample or Sample to Population for Z-tests of Proportions

Which problem type are you working on?

Sample to Sample or Sample to Population for Z-tests of Proportions

Which problem type are you working on?

Sample to Sample

Sample to Population

Sample to Sample or Sample to Population for Z-tests of Proportions