Question

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

	column 1	column 2	column 3
row 1	137	86	77
row 2	93	51	86
row 3	126	76	112

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

H0: Rows and columns are: Independent or dependent

H1: Rows and columns are: Independent or dependent

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 α=0.01, find the critical value of χ2. Specify the rejection and nonrejection regions on the chi-square distribution curve.

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

χ2=_______
The rejection region is (On the right? or On the left?) of the critical value of χ2.

The nonrejection region is (on the right? or on the left?) of the critical value of χ2.

d. Find the value of the test statistic χ2.

Round your answer to three decimal places.

The value of the test statistic χ2 is _________.

e. Using α=0.01, would you reject the null hypothesis? (yes or no).

Answer 1

a: The null and alternative hypotheses for a test of independence for this table.

H0: Rows and columns are Independent.

H1: Rows and columns are dependent.

b. The expected frequencies for all cells assuming that the null hypothesis is true.

c: For α=0.01, the critical value of χ2 is 13.277.

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

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

χ2= 10.6850

The rejection region is On the right of the critical value of χ2.

The nonrejection region is on the left of the critical value of χ2.

d. Find the value of the test statistic χ2.

Round your answer to three decimal places.

The value of the test statistic χ2 is 10.685.

e. Using α=0.01, would you reject the null hypothesis. no