You are conducting a test of the claim that the row variable and the column vari

Question

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

Give all answers rounded to 3 places after the decimal point, if necessary.

(a) Enter the expected frequencies below:

(b) What is the chi-square test-statistic for this data?
      Test Statistic: 2=

(c) What is the critical value for this test of independence when using a significance level of = 0.025?
      Critical Value: 2=

(d) What is the correct conclusion of this hypothesis test at the 0.025 significance level?

There is sufficient evidence to support the claim that the row and column variables are dependent.

There is sufficient evidence to warrant rejection of the claim that the row and column variables are dependent.

There is not sufficient evidence to support the claim that the row and column variables are dependent.

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.

X Y Z A 9 66 36 B 11 35 65

Explanation / Answer

Ans:

a)

b)Test statistic=18.042

df=(2-1)*(3-1)=2

c)Critical chi square=CHIINV(0.025,2)=7.378

d)As,test statistic>7.378,we reject null hypothesis.

There is sufficient evidence to support the claim that the row and column variables are dependent.

Observed(O) X Y Z Total A 9 66 36 111 B 11 35 65 111 Total 20 101 101 222 Expected(E) X Y Z Total A 10 50.5 50.5 111 B 10 50.5 50.5 111 Total 20 101 101 222 Chi square=(O-E)^2/E X Y Z Total A 0.100 4.757 4.163 9.021 B 0.100 4.757 4.163 9.021 Total 0.200 9.515 8.327 18.042

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