Question

# (1 point) Use software to test the null hypothesis of whether there is a relationship between...

(1 point) Use software to test the null hypothesis of whether there is a relationship between the two classifications, A and B, of the 3×33×3 contingency table shown below. Test using α=0.05α=0.05. NOTE: You may do this by hand, but it will take a bit of time.

 B1B1 B2B2 B3B3 Total A1A1 5454 4343 6868 165165 A2A2 5959 6565 7272 196196 A3A3 7575 6969 6565 209209 Total 188188 177177 205205 570570

(a)  χ2=χ2=

(b) Find the degrees of freedom.

(c) Find the critical value.  χ2=χ2=

(d) The final conclusion is

A. We can reject the null hypothesis that A and B are not related and accept that there seems to be a relationship between A and B.
B. There is not sufficient evidence to reject the null hypothesis that there is no relationship between A and B.

a)

 Applying chi square test of independence:
 Expected Ei=row total*column total/grand total B1 B2 B3 Total A1 54.42 51.24 59.34 165 A2 64.65 60.86 70.49 196 A3 68.93 64.90 75.17 209 total 188 177 205 570 chi square    χ2 =(Oi-Ei)2/Ei B1 B2 B3 Total A1 0.003 1.324 1.263 2.5906 A2 0.493 0.281 0.032 0.8065 A3 0.534 0.259 1.375 2.1680 total 1.0302 1.8643 2.6706 5.5651 test statistic X2 = 5.5651

b)

 degree of freedom(df) =(rows-1)*(columns-1)= 4

c)

 for 4 df and 0.05 level , critical value       χ2= 9.4877

d)

B. There is not sufficient evidence to reject the null hypothesis that there is no relationship between A and B.

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