Question 1:

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	10
B	8
C	23
D	8
E	18

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 2:

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	43	32	38
B	32	53	23

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= 0.005? Critical Value:2=___(Enter 10.597 as the answer to this question.)

(d) What is the correct conclusion of this hypothesis test at the 0.005 significance level?

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

You wish to test the following claim: A population of weights has the last digit (ones-digit) that do NOT occur with the same frequency.

Which of the following would be your hypotheses?

1. H0:Proportion is not independent of digit. H1:Proportion is independent of digit.
2. H0:The proportion of each digit occuring is the same. H1:The proportion of each digit occuring is NOT the same.
3. H0:The proportion of each digit occuring is NOT the same. H1:The proportion of each digit occuring is the same.
4. H0:Proportion is independent of digit. H1:Proportion is not independent of digit.

____________________________________________________________________________

Question 4:

You are given a contingency table laying out the success and failure amounts of various treatments for a disease.

You wish to test the following claim that success of the treatment is independent of the type of treatment.

Which of the following would be your hypotheses?

1. H0:The proportion of success is NOT the same in each treatment.

H1: The proportion of success is the same in each treatment.

1. H0:The proportion of success is the same in each treatment.

H1: The proportion of success is NOT the same in each treatment.

1. H0: Success is independent of treatment.

H1: Success and treatment are dependent.

1. H0: Success and treatment are dependent.

H1: Success is independent of treatment.<

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Question 5:

You are conducting a multinomial hypothesis test (= 0.05) for the claim that all 5 categories are equally likely to be selected.

The p-value for this sample is 0.6399

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 6:

You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table.

	XX	ZY	ZZ
AA	49	31	15
BB	63	45	10

The chi-squaretest-statistic for this data is 2.879.

Thecritical value for this test of independence when using a significance level of= 0.05 is2= 5.991.

What is the correct conclusion of this hypothesis test at the 0.05 significance level?

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

____________________________________________________________________________

Question 7:

You are conducting a multinomial hypothesis test (= 0.05) for the claim that all 5 categories are equally likely to be selected.

The p-value for this sample is 0.0182

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 8:

You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table.

	XX	YY	ZZ
AA	52	26	19
BB	45	26	28

The chi-squaretest-statistic for this data is 2.208.

Thecritical value for this test of independence when using a significance level of = 0.005 is2=10.597.

What is the correct conclusion of this hypothesis test at the 0.005 significance level?

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

____________________________________________________________________________

Question 9:

You intend to conduct a goodness-of-fit test for a multinomial distribution with 5 categories. You collect data from 79 subjects.

What are the degrees of freedom for the2distribution for this test?

d.f. = ____

____________________________________________________________________________

Question 10:

You intend to conduct a test of independence for a contingency table with 7 categories in the column variable and 2 categories in the row variable. You collect data from 312 subjects.

What are the degrees of freedom for the2 distribution for this test?

d.f. =____

____________________________________________________________________________

Question 11:

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	13
C	23
D	8
E	12

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.