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?

1. Reject the Null Hypothesis
2. 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...

1. less than (or equal to)
2. greater than

This test statistic leads to a decision to...

1. reject the null
2. accept the null
3. fail to reject the null
4. accept the alternative

As such, the final conclusion is that...

1. There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.
2. There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.
3. The sample data support the claim that all 5 categories are equally likely to be selected.
4. 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?

1. Fail to reject the Null Hypothesis
2. 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:

1. Enter the observed matrix into the calculator, per the Technology Corner.
2. Perform the test, per the Technology Corner.
3. 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?

1. There isnot sufficient evidence tosupport the claim that the row and column variables are dependent.
2. There isnot sufficient evidence to warrantrejection of the claim that the row and column variables are dependent.
3. Thereis sufficient evidence tosupport the claim that the row and column variables are dependent.
4. 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:

1. Enter the observed matrix into the calculator, per the Technology Corner.
2. Perform the test, per the Technology Corner.
3. 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?

1. There isnot sufficient evidence tosupport the claim that the row and column variables are dependent.
2. There isnot sufficient evidence to warrantrejection of the claim that the row and column variables are dependent.
3. Thereis sufficient evidence tosupport the claim that the row and column variables are dependent.
4. 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:

1. Enter the observed matrix into the calculator, per the Technology Corner.
2. Perform the test, per the Technology Corner.
3. 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?

1. There isnot sufficient evidence tosupport the claim that the row and column variables are dependent.
2. There isnot sufficient evidence to warrantrejection of the claim that the row and column variables are dependent.
3. Thereis sufficient evidence tosupport the claim that the row and column variables are dependent.
4. 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:

1. Enter the observed matrix into the calculator, per the Technology Corner.
2. Perform the test, per the Technology Corner.
3. 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?

1. There isnot sufficient evidence tosupport the claim that the row and column variables are dependent.
2. There isnot sufficient evidence to warrantrejection of the claim that the row and column variables are dependent.
3. Thereis sufficient evidence tosupport the claim that the row and column variables are dependent.
4. 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.