Question
Question 12: You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies: Ho:pA=0.15;
Question 12:
You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:
Ho:pA=0.15; pB=0.15; pC=0.3;pD=0.4
Complete the table. Report all answers accurate to three decimal places.
Category | Observed Frequency | Expected Frequency |
A | 29 | |
B | 40 | |
C | 48 | |
D | 37 |
What is the chi-square test-statistic for this data?
2=___
What is the P-Value?
P-Value = ___
For significance level alpha 0.01, what would be the conclusion of this hypothesis test?
- Reject the Null Hypothesis
- Fail to reject the Null Hypothesis
____________________________________________________________________________
Question 13:
You are conducting a multinomial hypothesis test ( = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table.
Category | Observed Frequency | Expected Frequency | |
A | 6 | ||
B | 7 | ||
C | 21 | ||
D | 15 | ||
E | 24 |
What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places.)
2=____
What are the degrees of freedom for this test?
d.f.= ____
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value = ____
The p-value is...
- less than (or equal to)
- greater than
This test statistic leads to a decision to...
- reject the null
- accept the null
- fail to reject the null
- accept the alternative
As such, the final conclusion is that...
- There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.
- There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.
- The sample data support the claim that all 5 categories are equally likely to be selected.
- There is not sufficient sample evidence to support the claim that all 5 categories are equally likely to be selected.
____________________________________________________________________________
Question 14:
You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:
Ho :pA=0.4; pB=0.1; pC=0.3; pD=0.2
Complete the table. Report all answers accurate to three decimal places.
Category | Observed Frequency | Expected Frequency |
A | 50 | |
B | 24 | |
C | 28 | |
D | 34 |
What is the chi-square test-statistic for this data?
2=___
What is the P-Value?
P-Value = ____
For significance level alpha 0.1, what would be the conclusion of this hypothesis test?
- Fail to reject the Null Hypothesis
- Reject the Null Hypothesis
____________________________________________________________________________
Question 15:
You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table.
X | Y | Z | |
A | 41 | 7 | 41 |
B | 21 | 70 | 19 |
Give all answers rounded to3 places after the decimal point, if necessary.
(a) Enter theexpected frequencies below:
X | Y | Z | |
A | |||
B |
To find the expected frequencies:
- Enter the observed matrix into the calculator, per the Technology Corner.
- Perform the test, per the Technology Corner.
- Return to the matrix menu and view the B matrix. This will be the expected frequencies.
(b) What is the chi-squaretest-statistic for this data?
Test Statistic:2= ____
(c) What is thecritical value for this test of independence when using a significance level of= 0.10? Critical Value:2=___(Enter 4.605 as the answer to this question.)
(d) What is the correct conclusion of this hypothesis test at the 0.10 significance level?
- There isnot sufficient evidence tosupport the claim that the row and column variables are dependent.
- There isnot sufficient evidence to warrantrejection of the claim that the row and column variables are dependent.
- Thereis sufficient evidence tosupport the claim that the row and column variables are dependent.
- Thereis sufficient evidence to warrantrejection of the claim that the row and column variables are dependent.
Remember to give all answers rounded to3 places after the decimal point, if necessary.
____________________________________________________________________________
Question 16:
You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table.
X | Y | Z | |
A | 46 | 14 | 38 |
B | 54 | 28 | 38 |
Give all answers rounded to3 places after the decimal point, if necessary.
(a) Enter theexpected frequencies below:
X | Y | Z | |
A | |||
B |
To find the expected frequencies:
- Enter the observed matrix into the calculator, per the Technology Corner.
- Perform the test, per the Technology Corner.
- Return to the matrix menu and view the B matrix. This will be the expected frequencies.
(b) What is the chi-squaretest-statistic for this data?
Test Statistic:2= ____
(c) What is thecritical value for this test of independence when using a significance level of= 0.10? Critical Value:2=___(Enter 4.605 as the answer to this question.)
(d) What is the correct conclusion of this hypothesis test at the 0.10 significance level?
- There isnot sufficient evidence tosupport the claim that the row and column variables are dependent.
- There isnot sufficient evidence to warrantrejection of the claim that the row and column variables are dependent.
- Thereis sufficient evidence tosupport the claim that the row and column variables are dependent.
- Thereis sufficient evidence to warrantrejection of the claim that the row and column variables are dependent.
Remember to give all answers rounded to3 places after the decimal point, if necessary.
____________________________________________________________________________
Question 17:
You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table.
X | Y | Z | |
A | 35 | 43 | 36 |
B | 44 | 18 | 34 |
Give all answers rounded to3 places after the decimal point, if necessary.
(a) Enter theexpected frequencies below:
X | Y | Z | |
A | |||
B |
To find the expected frequencies:
- Enter the observed matrix into the calculator, per the Technology Corner.
- Perform the test, per the Technology Corner.
- Return to the matrix menu and view the B matrix. This will be the expected frequencies.
(b) What is the chi-squaretest-statistic for this data?
Test Statistic:2= ____
(c) What is thecritical value for this test of independence when using a significance level of= 0.10? Critical Value:2=___(Enter 4.605 as the answer to this question.)
(d) What is the correct conclusion of this hypothesis test at the 0.10 significance level?
- There isnot sufficient evidence tosupport the claim that the row and column variables are dependent.
- There isnot sufficient evidence to warrantrejection of the claim that the row and column variables are dependent.
- Thereis sufficient evidence tosupport the claim that the row and column variables are dependent.
- Thereis sufficient evidence to warrantrejection of the claim that the row and column variables are dependent.
Remember to give all answers rounded to3 places after the decimal point, if necessary.
____________________________________________________________________________
Question 18:
You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table.
X | Y | Z | |
A | 54 | 26 | 28 |
B | 26 | 36 | 19 |
Give all answers rounded to3 places after the decimal point, if necessary.
(a) Enter theexpected frequencies below:
X | Y | Z | |
A | |||
B |
To find the expected frequencies:
- Enter the observed matrix into the calculator, per the Technology Corner.
- Perform the test, per the Technology Corner.
- Return to the matrix menu and view the B matrix. This will be the expected frequencies.
(b) What is the chi-squaretest-statistic for this data?
Test Statistic:2= ____
(c) What is thecritical value for this test of independence when using a significance level of= 0.01? Critical Value:2=___(Enter 4.605 as the answer to this question.)
(d) What is the correct conclusion of this hypothesis test at the 0.01 significance level?
- There isnot sufficient evidence tosupport the claim that the row and column variables are dependent.
- There isnot sufficient evidence to warrantrejection of the claim that the row and column variables are dependent.
- Thereis sufficient evidence tosupport the claim that the row and column variables are dependent.
- Thereis sufficient evidence to warrantrejection of the claim that the row and column variables are dependent.
Remember to give all answers rounded to3 places after the decimal point, if necessary.
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