A company is considering adding a new ingredient to its bread recipe to increase the freshness of the bread. To study the impact of adding ingredient P, Q, R, S, or T to the recipe, they baked 270 loaves of bread. Some of the loaves contained no extra ingredients, while each of the rest contained one of the five new ingredients. The freshness of the bread was checked one week later, and the results were used to create the two-way tables below.

Question

Which tables suggest an association between adding an extra ingredient and the freshness of the bread? Select the three correct answers.
A 3-column table with 2 rows titled Effect of Ingredient P on Freshness. Column 1 has entries Contains the Ingredient, Does not Contain the Ingredient. Column 2 is labeled Stays Fresh with entries 11, 4. Column 3 is labeled Does not stay fresh with entries 39, 16.
A 3-column table with 2 rows titled Effect of Ingredient Q on Freshness. Column 1 has entries Contains the Ingredient, Does not Contain the Ingredient. Column 2 is labeled Stays Fresh with entries 9, 4. Column 3 is labeled Does not stay fresh with entries 41, 16.
A 3-column table with 2 rows titled Effect of Ingredient R on Freshness. Column 1 has entries Contains the Ingredient, Does not Contain the Ingredient. Column 2 is labeled Stays Fresh with entries 16, 4. Column 3 is labeled Does not stay fresh with entries 34, 16.
A 3-column table with 2 rows titled Effect of Ingredient S on Freshness. Column 1 has entries Contains the Ingredient, Does not Contain the Ingredient. Column 2 is labeled Stays Fresh with entries 4, 4. Column 3 is labeled Does not stay fresh with entries 46, 16.
A 3-column table with 2 rows titled Effect of Ingredient T on Freshness. Column 1 has entries Contains the Ingredient, Does not Contain the Ingredient. Column 2 is labeled Stays Fresh with entries 34, 4. Column 3 is labeled Does not stay fresh with entries 16, 16.

Answer 1

To determine which tables suggest an association between adding an extra ingredient and the freshness of the bread, we can look at the differences in the freshness outcomes for the loaves that contained the ingredient versus those that did not contain the ingredient.

1. Ingredient P:

   • Stays Fresh: 11 (Contains P), 4 (Does not contain P)
   • Does not stay fresh: 39 (Contains P), 16 (Does not contain P)
   • Here, there is a noticeable difference (relatively higher value) in the amount that stays fresh compared to those that do not stay fresh when P is added.

2. Ingredient Q:

   • Stays Fresh: 9 (Contains Q), 4 (Does not contain Q)
   • Does not stay fresh: 41 (Contains Q), 16 (Does not contain Q)
   • There is also a slight difference favoring those that use Ingredient Q, but it isn't substantial.

3. Ingredient R:

   • Stays Fresh: 16 (Contains R), 4 (Does not contain R)
   • Does not stay fresh: 34 (Contains R), 16 (Does not contain R)
   • This shows a significant difference, suggesting that Ingredient R may be highly effective in preserving freshness.

4. Ingredient S:

   • Stays Fresh: 4 (Contains S), 4 (Does not contain S)
   • Does not stay fresh: 46 (Contains S), 16 (Does not contain S)
   • This indicates no association, as the stays fresh counts are equal, while the does not stay fresh counts are substantially higher when Ingredient S is included.

5. Ingredient T:

   • Stays Fresh: 34 (Contains T), 4 (Does not contain T)
   • Does not stay fresh: 16 (Contains T), 16 (Does not contain T)
   • A marked difference suggests that Ingredient T is also significantly effective.

From this analysis, the tables that suggest an association between adding an extra ingredient and the freshness of the bread are:

• Ingredient P
• Ingredient R
• Ingredient T

Therefore, the correct answers are the tables for ingredients P, R, and T.