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Chapter 12 Assignment Assignment: Chapter 12 Assignment Assignment Score: 0.00% Save Submit Assignment for Grading Questions

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2.

According to the question,

A B C marginal total
P 40 50 45 135
Q 10 20 35 65
marginal total 50 70 80 200

So, we are to test, H0: Row variables & column variables are independent of each other vs. H1: Row variables & column variables are not independent

For testing of independence we use chi-square test statistic given by--

\chi ^2= \sum \frac{(O_{ij}- E_{ij})^2}{E_{ij}} with degrees of freedom (r-1)*(c-1) , where r & c are the number of rows & columns

and O_{ij} is observed frequency of (i.j)thcell and E_{ij}= \frac{f_{i.}f_{.j}}{N} is expected frequency of (i.j)thcell  and N= total frequency,

Then, expected frequencies are as follows--

A B C marginal total
P 33.75 47.25 54 135
Q 16.25 22.75 26 65
marginal total 50 70 80 200

Then,

\chi ^2= \frac{(40- 33.75)^2}{33.75}+\frac{(10- 16.25)^2}{16.25}+\frac{(50- 47.25)^2}{47.25}+\frac{(20- 22.75)^2}{22.75}+\frac{(54- 45)^2}{54}+\frac{(35- 26)^2}{26}

\chi ^2= 8.8812\approx 8.88 with degrees of freedom =(3-1)*(2-1)=2

The P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than 8.88

Now, P(\chi ^2 > 8.88) =0.01 which is less than significance level \alpha= 0.05

So, we cannot accept null hypothesis indicating there is some dependence among row variables & column variables.

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