Question

Chapter 11, Section 11.3, Problem 021 Consider the following contingency table that is based on a sample survey. Column 1 Column 2 Column 3 Row 1 133 83 84 Row 2 90 52 | 91 | Row 3 1367996 a. Write the null and alternative hypotheses for a test of independence for this table. Ho: Rows and columns are H: Row and columns are b. Calculate the expected frequencies for all cells assuming that the null hypothesis is true.

Answer 1

Ho: independent

Ha : dependent

b)

Expected	Ei=row total*column total/grand total	column 1	column 2	column 3
	row 1	127.607	76.066	96.327
	row 2	99.108	59.078	74.814
	row 3	132.286	78.855	99.859

c)

degree of freedom(df) =(rows-1)*(columns-1)=		4
for 4 df and 0.01 level , critical value       χ2=		13.277

rejection region is to the right of the critical value of X^2

non rejection region is to the left of the critical value of X^2

d)

test statistic X2 =

7.878

e)

No