The two-way table below describes the quality of sweatshirts and T-shirts screen printed at a local store.

Question

Quality of Screen Printing by Item Type


Perfect
Flawed
T-Shirts
90
6
Sweatshirts
40
10

Which statement best describes the relationship between the two variables?
There is an association because the relative frequencies by row are different.
There is an association because the relative frequencies by row are the same.
There is no association because the relative frequencies by row are different.
There is no association because the relative frequencies by row are the same.

Answer 1

To determine the association between the quality of screen printing (Perfect or Flawed) and the item type (T-Shirts or Sweatshirts), we can calculate the relative frequencies by row.

1. For T-Shirts:

   • Total T-Shirts = 90 (Perfect) + 6 (Flawed) = 96
   • Proportion Perfect T-Shirts = 90 / 96 = 0.9375 or 93.75%
   • Proportion Flawed T-Shirts = 6 / 96 = 0.0625 or 6.25%

2. For Sweatshirts:

   • Total Sweatshirts = 40 (Perfect) + 10 (Flawed) = 50
   • Proportion Perfect Sweatshirts = 40 / 50 = 0.8 or 80%
   • Proportion Flawed Sweatshirts = 10 / 50 = 0.2 or 20%

Now we can compare the relative frequencies:

• T-Shirts: 93.75% Perfect, 6.25% Flawed
• Sweatshirts: 80% Perfect, 20% Flawed

The relative frequencies of perfect and flawed printings are different for T-shirts and Sweatshirts, indicating that the quality of screen printing depends on the item type.

Given this information, the correct statement that describes the relationship between the two variables is:

There is an association because the relative frequencies by row are different.