Question

Suppose we want to explore if there is significant evidence of difference among Category A, B, and C in the proportion of Level 1 for certain characteristic.

A B C Total
Level 1 50 90 225 365
Level 2 150 210 275 635
Total 200 300 500 1000
At significant level 0.05, test the equality of proportion of Level 1 for category A, B and C. If needed, perform the Marascuilo procedure for pairwise comparisons. Show your work.

Answer 1

Kindly check explanation (since we need to show how the work is done) but what can be noticed is that there is a proportional difference between the 3.

Explanation:

Know that Vo :ht = 1//3, where t = 1,2,3.

(1). The expected values for levels A, B and C = 0.33 which is a total of 100%.

The observed values = 50, 90, and 225 with a total of 365.

The expected values = 121.67 for the three categories which gives us a total of 365.

For the three categories, the differences between the observed values and the expected values are -71.67, -31.67 and 103.33.

(2). Thus, the value for the test statistics is = (observed values - expected values)^2/ expected values.

So, for the three categories (A,B and C) we have; 42.217, 8.244 and 87.754. The total = 138.215.

Therefore the critical value = 5.991.

(3). We have to reject the null hypothesis Because 138.215 is greater than 5.991.

(4). For Marascuilo, we have;

Proportion

Group 1 - group 2 = 0.05(absolute difference) and 0.099050609( critical range) which is insignificant.

Group 1 - group 3 = 0.2( absolute difference) and 0.092643256(critical range) which is significant.

Group 2 - group 3 = 0.15(absolute difference) and 0.084615602(critical range) which is also significant.