Question

Chapter 12 Assignment Assignment: Chapter 12 Assignment Assignment Score: 0.00% Save Submit Assignment for Grading Questions Exercise 12.07 (Self-Test) Algorithmic <Question 2 of 4 Check My Work (7 remaining) eBook Video The following table contains observed frequencies for a sample of 200. Column Variable Row Variable - Q Test for independence of the row and column variables using a = .05 . Compute the value of the x test statistic (to 2 decimals). A B C 40 50 45 10 20 35 The p-value is - Select your answer - 7 What is your conclusion? - Select your answer - Check My Work (7 remaining)

Answer 1

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 , where r & c are the number of rows & columns

and $O_{ij}$ is observed frequency of (i.j)^thcell and is expected frequency of (i.j)^thcell  and N= total frequency,

N

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.