You are conducting a test of the claim that the row variables and the column variables are dependent in the following contingency table. Ho: The variables are independent Ha: At least two variables are dependent (Claim) Y. A 50 49 14 B 41 47 31 Expected Frequencies (row i and column j) (Total;) (Total) E j= Total

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You are conducting a test of the claim that the row variables and the column variables are dependent in
the following contingency table.
Ho: The variables are independent
Ha: At least two variables are dependent (Claim)
Y
50
49
14
41
47
31
Expected Frequencies (row i and column j)
(Total;) (Total;)
E..j=
Total
Give all answers rounded to 3 places after the decimal point, if necessary.
(a) Enter the expected frequencies below:
Y
B
Residual Values
(Row i and
column j)
Chi Square Test Statistic
Degrees of Freedom
(0- E)
(0.,- E. ) x =
E.
R, df = (#ofRows – 1)(#ofColumns – 1)
(b) Enter the Residual Values below:
Y
Transcribed Image Text:You are conducting a test of the claim that the row variables and the column variables are dependent in the following contingency table. Ho: The variables are independent Ha: At least two variables are dependent (Claim) Y 50 49 14 41 47 31 Expected Frequencies (row i and column j) (Total;) (Total;) E..j= Total Give all answers rounded to 3 places after the decimal point, if necessary. (a) Enter the expected frequencies below: Y B Residual Values (Row i and column j) Chi Square Test Statistic Degrees of Freedom (0- E) (0.,- E. ) x = E. R, df = (#ofRows – 1)(#ofColumns – 1) (b) Enter the Residual Values below: Y
Residual Values
(Row I and
column j)
Chi Square Test Statistic
Degrees of Freedom
(0.j- E)x
(0-E)
R df (#of Rows
1)(#ofColumns- 1)
%3D
%3D
E
(b) Enter the Residual Values below:
Y
A.
(c) What is the chi-square test-statistic for this data?
Test Statistic: X =
(d) What is the critical value for this test of independence when using a significance level of a - 0.025?
Critical Value: X
(e) What is the correct conclusion of this hypothesis test at the 0.025 significance level?
O There is sufficient evidence to support the claim that the row and column variables are dependent.
O There is not sufficient evidence to support the claim that the row and column variables are
dependent.
O There is sufficient evidence to warrant rejection of the claim that the row and column variables are
dependent.
O There is not sufficient evidence to warrant rejection of the claim that the row and column variables
are dependent.
Remember to give all answers rounded to 3 places after the decimal point, if necessary.
Transcribed Image Text:Residual Values (Row I and column j) Chi Square Test Statistic Degrees of Freedom (0.j- E)x (0-E) R df (#of Rows 1)(#ofColumns- 1) %3D %3D E (b) Enter the Residual Values below: Y A. (c) What is the chi-square test-statistic for this data? Test Statistic: X = (d) What is the critical value for this test of independence when using a significance level of a - 0.025? Critical Value: X (e) What is the correct conclusion of this hypothesis test at the 0.025 significance level? O There is sufficient evidence to support the claim that the row and column variables are dependent. O There is not sufficient evidence to support the claim that the row and column variables are dependent. O There is sufficient evidence to warrant rejection of the claim that the row and column variables are dependent. O There is not sufficient evidence to warrant rejection of the claim that the row and column variables are dependent. Remember to give all answers rounded to 3 places after the decimal point, if necessary.
Expert Solution
Step 1

Chi-Square test of Independence:

(a) 

The table of data is given as:

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