Null hypothesis for a chi-square goodness of fit test

1. Null-hypothesis for a
Chi-Square Goodness of Fit Test

2. With hypothesis testing we are setting up a null-hypothesis
–

3. With hypothesis testing we are setting up a null-hypothesis
– the probability that there is no effect or
relationship –

4. With hypothesis testing we are setting up a null-hypothesis
– the probability that there is no effect or
relationship – and then we collect evidence that leads
us to either accept or reject that null hypothesis.

5. As you may recall, a Chi-square Goodness of Fit test is a
method that tests the degree to which the distribution
of a nominal variable (e.g., gender, political affiliation,
ethnic group, levels of age, etc.) from a sample fits the
hypothesized distribution.

6. Example

7. Problem
A public opinion poll surveyed a simple random sample of 1000
voters in the blue state of Connecticut. Respondents were asked
to share their party affiliation (Republican or Democrat)
Results are shown in the table below.
Respondents were asked to share their party affiliation
(Republican or Democrat)
Results are shown in the table below.
The expectation is that the distribution would be even or 50/50.
To what degree does the sample distribution fit the expected
distribution?

8. Problem
A public opinion poll surveyed a simple random sample of 1000
voters in the blue state of Connecticut. Respondents were asked
to share their party affiliation (Republican or Democrat)
Results are shown in the table below.
Respondents were asked to share their party affiliation
(Republican or Democrat)
Results are shown in the table below.
The expectation is that the distribution would be even or 50/50.
To what degree does the sample distribution fit the expected
distribution?

9. Problem
A public opinion poll surveyed a simple random sample of 1000
voters in the blue state of Connecticut. Respondents were asked
to share their party affiliation (Republican or Democrat)
Results are shown in the table below.
Results are shown in the table below.
The expectation is that the distribution would be even or 50/50.
To what degree does the sample distribution fit the expected
distribution?

10. Problem
A public opinion poll surveyed a simple random sample of 1000
voters in the blue state of Connecticut. Respondents were asked
to share their party affiliation (Republican or Democrat)
Results are shown in the table below.
Party Affiliation
Results are shown in the table below.
Republican Democrat
320 680
The expectation is that the distribution would be even or 50/50.
To what degree does the sample distribution fit the expected
distribution?

11. Problem
A public opinion poll surveyed a simple random sample of 1000
voters in the blue state of Connecticut. Respondents were asked
to share their party affiliation (Republican or Democrat)
Results are shown in the table below.
Party Affiliation
Results are shown in the table below.
Republican Democrat
320 680
The expectation is that the distribution would be even or 40/60.
To what degree does the sample distribution fit the expected
distribution?

12. Problem
A public opinion poll surveyed a simple random sample of 1000
voters in the blue state of Connecticut. Respondents were asked
to share their party affiliation (Republican or Democrat)
Results are shown in the table below.
Party Affiliation
Republican Democrat
320 680
The expectation is that the distribution would be even or 40/60.
To what degree does the sample distribution fit the expected
distribution?

13. Here is a template for writing a null-hypothesis for a
Chi-square Goodness of Fit Test:

14. Here is a template for writing a null-hypothesis for a
Chi-square Goodness of Fit Test:
The [Insert Category Heading] of [Insert Nominal
Variable] occur with a [Insert Probability].

15. Let’s go back to our problem:

16. Problem
A public opinion poll surveyed a simple random sample of 1000
voters in the blue state of Connecticut. Respondents were asked
to share their party affiliation (Republican or Democrat)
Results are shown in the table below.
Party Affiliation
Republican Democrat
320 680
The expectation is that the distribution would be even or 40/60.
To what degree does the sample distribution fit the expected
distribution?

17. Problem
A public opinion poll surveyed a simple random sample of 1000
voters in the blue state of Connecticut. Respondents were asked
to share their party affiliation (Republican or Democrat)
Results are shown in the table below.
Party Affiliation
Republican Democrat
320 680
The expectation is that the distribution would be even or 40/60.
To what degree does the sample distribution fit the expected
distribution?
The null-hypothesis: The [Insert Category Heading] of
[Insert Categories] occur at a [Insert Hypothesized
Probability] probability in Connecticut.

18. Problem
A public opinion poll surveyed a simple random sample of 1000
voters in the blue state of Connecticut. Respondents were asked
to share their party affiliation (Republican or Democrat)
Results are shown in the table below.
Party Affiliation
Republican Democrat
320 680
The expectation is that the distribution would be even or 40/60.
To what degree does the sample distribution fit the expected
distribution?
The null-hypothesis: The [Insert Category Heading] of
[Insert Categories] occur at a [Insert Hypothesized
Probability] probability in Connecticut.

19. Problem
A public opinion poll surveyed a simple random sample of 1000
voters in the blue state of Connecticut. Respondents were asked
to share their party affiliation (Republican or Democrat)
Results are shown in the table below.
Party Affiliation
Republican Democrat
320 680
The expectation is that the distribution would be even or 40/60.
To what degree does the sample distribution fit the expected
distribution?
The null-hypothesis: The party affiliation of [Insert
Categories] occur at a [Insert Hypothesized Probability]
probability in Connecticut.

20. Problem
A public opinion poll surveyed a simple random sample of 1000
voters in the blue state of Connecticut. Respondents were asked
to share their party affiliation (Republican or Democrat)
Results are shown in the table below.
Party Affiliation
Republican Democrat
320 680
The expectation is that the distribution would be even or 40/60.
To what degree does the sample distribution fit the expected
distribution?
The null-hypothesis: The party affiliation of Republican /
Democrat occur at a [Insert Hypothesized Probability]
probability in Connecticut.

21. Problem
A public opinion poll surveyed a simple random sample of 1000
voters in the blue state of Connecticut. Respondents were asked
to share their party affiliation (Republican or Democrat)
Results are shown in the table below.
Party Affiliation
Republican Democrat
320 680
The expectation is that the distribution would be even or 40/60.
To what degree does the sample distribution fit the expected
distribution?
The null-hypothesis: The party affiliation of Republican /
Democrat occur at a .4/.6 probability in Connecticut.

22. Here is a template:

23. Here is a template:
The null-hypothesis: The [Insert Category Heading] of
[Insert Categories] occur at a [Insert Hypothesized
Probability] probability.