Question

Consider the following contingency table that records the results obtained for four samples of fixed sizes selected from four populations.

	Population 1	Population 2	Population 3	Population 4
Row 1	38	86	91	72
Row 2	21	55	82	119
Row 3	33	42	80	104

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

H0: The proportion in each row is (the same? or Not the same?) for all four populations.

H1: The proportion in each row is (the same? or Not the same?) for all four populations

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

Round your answers to three decimal places, where required.

	Population 1	Population 1	Population 1	Population 1	Total
Row 1
Row 2
Row 3
Total

c. For α=0.025, 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=0.025, would you reject the null hypothesis? (Yes or No)

Answer 1

The statistical software output for this problem is :

(a)

H0: The proportion in each row is the same for all four populations.

H1: The proportion in each row is Not the same for all four populations

Critical value = 14.45

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

The non rejection region is on the left of the critical value of χ2.

The value of the test statistic χ2 is = χ2 = 32.228

Yes