Question

Researchers for a textile company carried out an experiment comparing the longevity of two new fabric blends.

They carried out a series of usage tests, known as double rubs, on 100 pieces of each type of material. These scales are used for this type of testing.

Fabric Grade Number of Double Rubs
(in thousands)
Heavy duty
Medium duty
Light duty
Delicate duty
After performing the tests on each fabric, researchers found that on average, fabric A lasted through 7,900 double rubs and fabric B lasted through 9,200 double rubs.

The marketing department wants to advertise that both fabrics are tested and approved for medium-duty use.

Which statements are true about this situation?

The sales department can refer to fabric A as a medium-duty fabric.
The sales department can refer to fabric B as a medium-duty fabric.
Fabric A is a more durable fabric because it has a lower double rub rating than fabric B.
Neither fabric meets the requirements of a medium-duty fabric.
Fabric B is a more durable fabric because it has a higher double rub rating than fabric A.

Answer 1

I’ll use the common grading cutoffs (thousands of double rubs):

- Heavy duty: 15+
- Medium duty: 9–15
- Light duty: 3–9
- Delicate: <3

Given the sample means (A = 7.9k, B = 9.2k):

- The sales department can refer to fabric A as a medium-duty fabric. — False. (7.9k is below the 9k medium cutoff.)
- The sales department can refer to fabric B as a medium-duty fabric. — True. (9.2k ≥ 9k, so B meets the medium threshold.)
- Fabric A is a more durable fabric because it has a lower double rub rating than fabric B. — False. (Lower double rub = less durable, not more.)
- Neither fabric meets the requirements of a medium-duty fabric. — False. (Fabric B does meet medium-duty.)
- Fabric B is a more durable fabric because it has a higher double rub rating than fabric A. — True.

If you have a different grading table, tell me the cutoffs and I’ll re-evaluate.