Consider the following contingency table that is based on a sample survey.

Column 1 column 2 column 3

Row 1: 140 87 73

Row 2: 91 48 98

Row 3: 127 78 110

a.Write the null and alternative hypotheses for a test of independence for this table.

H0

: Rows and columns are

a.) independent

b.) dependen

H1: Row and columns are

a.) dependent

b.) independent

.

b.Calculate the expected frequencies for all cells assuming that the null hypothesis is true. Round your answers to three decimal places, where required.

column 1 column 2 column 3 Total

Row 1 ____ ____ ____ ____

Row 2 ____ _____ ____ _____

Row 3 ____ _____ _____ _____

Total ____ _____ _____ _____

c.For=0.01

, find the critical value of2

. Specify the rejection and nonrejection regions on the chi-square distribution curve.

Enter the exact answer from the chi-square distribution table.

2=