Sample to sample or sample to population

1. When you are working with nominal proportional data,
Sample to Sample or Sample to Population for Z-tests of Proportions

2. 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

3. 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

4. Here are your options:
Sample to Sample or Sample to Population for Z-tests of Proportions

5. Here are your options:
Sample to Sample
Sample to Population
Sample to Sample or Sample to Population for Z-tests of Proportions

6. 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

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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. So, now we know that we are dealing with nominal
proportional data.
Sample to Sample or Sample to Population for Z-tests of Proportions

21. 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 vacuum
2 = not very satisfied with the
vacuum
Sample to Sample or Sample to Population for Z-tests of Proportions

22. 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 vacuum
2 = not very satisfied with the
vacuum
Sample to Sample or Sample to Population for Z-tests of Proportions

23. So, now we know that we are dealing with nominal
proportional data.
Sample to Sample or Sample to Population for Z-tests of Proportions

24. 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

25. 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

26. 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

27. 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

28. Here is the problem again:
Sample to Sample or Sample to Population for Z-tests of Proportions

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

39. 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

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

41. What does a sample to sample problem look like?
Sample to Sample or Sample to Population for Z-tests of Proportions

42. 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

43. 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

44. 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

45. 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

46. 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

47. 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

48. 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

49. 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

50. 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

51. 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 Sample
This is an example of a
Sample to Sample problem
Sample to Sample or Sample to Population for Z-tests of Proportions

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

53. Which problem type are you working on?
Sample to Sample or Sample to Population for Z-tests of Proportions

54. 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