I figured out question (a) However, I am having a problem coming up with the correct answer for (b). Can someone offer me some assistance. Thank you.

Question:
You receive the results of a paired-comparison preference these of four soft drinks from a sample of 200 persons. The results are as follows:

Koak Zip Pabze Mr.Pep

Koak ---- 50 115 35
Zip 150 --- 160 70
Pabze 85 40 --- 45
Mr.Pep 165 130 155 ---

a). How does these brands rank in overall preference in this sample?

Koak Zip Pabze Mr.Peepers
Total 400 220 430 150
RankOrder 2 3 1 1

b). Develop an interval scale for these four brands. The results are as followed.

Please explain clearly how you came up with the results.

To develop an interval scale for the four brands, we need to assign numerical values to each brand based on the preference rankings.

Here's a step-by-step guide on how to come up with the interval scale:

1. Start by assigning values to the highest-ranked brand, which in this case is Pabze. Since Pabze has a rank order of 1, we can assign it the value of 4 because there are four brands in total.

2. Move on to the second-highest ranked brand, which is a tie between Koak and Mr.Pep, both with a rank order of 2. To assign values to these brands, we can take the average of their ranks. In this case, the average of 2 and 2 is 2, so both Koak and Mr.Pep will be assigned the value of 2.

3. Finally, assign the remaining value to the lowest-ranked brand, which is Zip with a rank order of 3. Since Zip is the last-ranked brand, we can assign it the value of 1.

After following these steps, we have assigned values to each brand as follows:

Koak: 2
Zip: 1
Pabze: 4
Mr.Pep: 2

This interval scale allows us to compare and quantify the preference for each brand based on the ranking data.