Question

6 the purchasing habits of 1,000 grocery shoppers are noted. no association is found between the variables. fill in the empty portion of the table with values that would support this claim. explain your reasoning.

	bought milk	no milk bought
no eggs bought

Explanation:

Step1: Find total for "bought eggs"

Sum of "bought eggs" row: \( 422 + 228 = 650 \)

Step2: Find total for "no eggs bought"

Total shoppers: 1000, so "no eggs bought" total: \( 1000 - 650 = 350 \)

Step3: Find proportion of "bought milk" in "bought eggs"

Proportion: \( \frac{422}{650} \approx 0.649 \) (or 64.9%)

Step4: Calculate "bought milk" in "no eggs bought"

Using the same proportion (no association), so: \( 350 \times 0.649 \approx 227 \) (round to 228 for consistency, or 227)

Step5: Calculate "no milk bought" in "no eggs bought"

Subtract from "no eggs bought" total: \( 350 - 227 = 123 \) (or \( 350 - 228 = 122 \))

Let's check with exact ratios. The ratio of bought milk to total in bought eggs is \( \frac{422}{650} \), and in no eggs bought, let the bought milk be \( x \), no milk be \( 350 - x \). For no association, \( \frac{422}{650} = \frac{x}{350} \), so \( x = \frac{422 \times 350}{650} = \frac{422 \times 7}{13} \approx 227.08 \approx 227 \), then no milk is \( 350 - 227 = 123 \).

Alternatively, using column totals:
Total bought milk: Let "no eggs, bought milk" be \( x \), total bought milk is \( 422 + x \)
Total no milk bought: \( 228 + (350 - x) = 578 - x \)
Proportion of bought eggs in bought milk: \( \frac{422}{422 + x} \)
Proportion of bought eggs in no milk: \( \frac{228}{578 - x} \)
Set equal: \( \frac{422}{422 + x} = \frac{228}{578 - x} \)
Cross - multiply: \( 422(578 - x)=228(422 + x) \)
\( 422\times578-422x = 228\times422+228x \)
\( 422\times(578 - 228)=x(422 + 228) \)
\( 422\times350 = 650x \)
\( x=\frac{422\times350}{650}=\frac{422\times7}{13}\approx227 \)

So the table becomes:

	bought milk	no milk bought
no eggs bought	227	123	(or 228 and 122 for integer consistency)

Answer:

The "no eggs bought, bought milk" cell can be \( 227 \) (or \( 228 \)) and "no eggs bought, no milk bought" cell can be \( 123 \) (or \( 122 \)). For example, filling the table as:

	bought milk	no milk bought
no eggs bought	227	123

(The key is that the proportion of buying eggs is the same for those who bought milk and those who didn't, i.e., \( \frac{422}{422 + 227}\approx\frac{228}{228+123}\approx0.65 \))