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.

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.

Step-by-step 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.