Consider the following contingency table that records the results obtained for f

Question

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

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

H0: The proportion in each row is

for all four populations.

H1: 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.

c. For =0.025, find the critical value of 2. Specify the rejection and nonrejection regions on the chi-square distribution curve.

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

The rejection region is

of the critical value of 2.

The nonrejection region is

of the critical value of 2.

d. Find the value of the test statistic 2.

Round your answer to three decimal places.

e. Using =0.025, would you reject the null hypothesis?

Sample Selected From Population 1 Population 2 Population 3 Population 4 Row 1 38 88 97 58 Row 2 11 58 82 119 Row 3 42 41 79 90

Explanation / Answer

E - Table Matrix

Relative Freuency - Table

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

^2 Test Statistic =57.767                  
^2 degrees of freedom = ( r-1 ) * (c-1) = 3 * 2 = 6, ^2 tab = 14.449                  
^2 p_value =0                  
| ^2 tab | < | ^2 cal | i.e. Reject Ho                  
The proportion in each row is not the same for all four populations                  

A 38 88 97 58 281 A1 B 11 58 82 119 270 A2 C 42 41 79 90 252 A3 Totals 91 187 258 267 803 B1 B2 B3 B4

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