Question

Consider the following contingency table that records the results obtained for four samples of fixed sizes selected from four populations. Sample Selected From Population 1 Population 2 Population 3 Population 4 Row 1 43 82 110 51 Row 2 28 56 82 113 Row 3 28 49 60 121 a. Write the null and alternative hypotheses for a test of homogeneity for this table. H 0 : The proportion in each row is for all four populations. H 1 : The proportion in each row is 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 2 Population 3 Population 4 Total Row 1 Row 2 Row 3 Total c. For α = 0.025 , find the critical value of χ 2 . Specify the rejection and nonrejection regions on the chi-square distribution curve. Enter the exact answer from the chi-square distribution table. χ 2 = The rejection region is of the critical value of χ 2 . The nonrejection region is of the critical value of χ 2 . d. Find the value of the test statistic χ 2 . Round your answer to three decimal places. The value of the test statistic χ 2 is . e. Using α = 0.025 , would you reject the null hypothesis?

Answer 1

a) H 0 : The proportion in each row is same for all four populations

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

b)

Expected	Ei=row total*column total/grand total	Pop. 1	Pop. 2	Pop. 3	Pop. 4
	row 1	34.403	64.984	87.572	99.040
	row 2	33.561	63.394	85.429	96.616
	row 3	31.035	58.622	78.999	89.344

c)

critical value of X² =14.449

The rejection region is of the right of the critical value of χ 2 .

The nonrejection region is of the left of the critical value of χ 2 .

d) value of the test statistic χ 2 =58.011

e)reject the null hypothesis