Hi There, i need assistance on the following problem solving:
Ms. Earl and Mr. Grey are tea blenders. Together, they have come up with 9 slightly different varieties for new Orange Pekoe tea, and have reached the testing phase in the development process.
They recruit 10 members of the company to take part in the testing. Each person is given all nine tea varieties to taste, and then asked to rank them from 1 to 9 order of preference.
After the first few trials, Ms. Earl& Mr. Grey noticed a common complaint from the testers.
Ms. Earl thought “perhaps they should have given each tester only a few tea varieties to try – may be just 3 each?”
Mr Grey said “OK. But will we still be able to get meaningful results from our trials?”
Ms Earl replied that they can investigate.
They decide to start their investigation by considering a simpler hypothetical situation, involving just 5 varieties of Tea.
“Let’s see what happens if we use 5 testers,” Mr Grey says. We’ll assign each tester (numbered 1 to 5) a combination of 3 varieties (labelled A, B, C, D and E) to taste and rank. I’ll randomize the distribution by drawing the letters out of a Hat”
“That looks ok,“ said Ms Earl, “Each tea variety gets tested by at least one person. But …oh no!I’ve noticed a problem! Varieties A and B are never assigned to the same perso. That means that A and B are never compared and ranked under identical testing conditions!”
“Hmm. May be we need to be more systematic to ensure that every pair of varieties gets tried together by at least one person. Perhaps we could assign every possible combination of 3 tea varieties to different tester?”
Ms. Earl and Mr. Grey are tea blenders. Together, they have come up with 9 slightly different varieties for new Orange Pekoe tea, and have reached the testing phase in the development process.
They recruit 10 members of the company to take part in the testing. Each person is given all nine tea varieties to taste, and then asked to rank them from 1 to 9 order of preference.
After the first few trials, Ms. Earl& Mr. Grey noticed a common complaint from the testers.
Ms. Earl thought “perhaps they should have given each tester only a few tea varieties to try – may be just 3 each?”
Mr Grey said “OK. But will we still be able to get meaningful results from our trials?”
Ms Earl replied that they can investigate.
They decide to start their investigation by considering a simpler hypothetical situation, involving just 5 varieties of Tea.
“Let’s see what happens if we use 5 testers,” Mr Grey says. We’ll assign each tester (numbered 1 to 5) a combination of 3 varieties (labelled A, B, C, D and E) to taste and rank. I’ll randomize the distribution by drawing the letters out of a Hat”
Tester | 1 | 2 | 3 | 4 | 5 |
| Tea varieties | BDC | CEA | ACE | EBC | DBC |
“That looks ok,“ said Ms Earl, “Each tea variety gets tested by at least one person. But …oh no!I’ve noticed a problem! Varieties A and B are never assigned to the same perso. That means that A and B are never compared and ranked under identical testing conditions!”
“Hmm. May be we need to be more systematic to ensure that every pair of varieties gets tried together by at least one person. Perhaps we could assign every possible combination of 3 tea varieties to different tester?”
- Show with a calculation that the number of testers needed for this is 10.
decide to test? let this number be n