Worksheet titled "Two-Way Frequency Tables Practice" featuring a table and questions related to gender and shoe preference data.

Since I can't view images directly, I’ll help you solve the problem based on the information you've provided in your text. Let's work through the two-way frequency table and answer each question step by step.

We are given a two-way frequency table about students' shoe preferences (Nike vs. Adidas), categorized by gender (Boys and Girls). The table is partially filled:

```
Prefer Nike Prefer Adidas TOTAL
Boys 3 19 35
Girls ? ? ?
TOTAL 31 20 51
```

Let’s first complete the table using the given totals.

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Step 1: Complete the Table

We know:
- Total number of students = 51
- Total who prefer Nike = 31
- Total who prefer Adidas = 20
- Total boys = 35
- Boys who prefer Nike = 3
- Boys who prefer Adidas = 19

So:
- Girls who prefer Nike = Total Nike - Boys who prefer Nike
= 31 - 3 = 28

- Girls who prefer Adidas = Total Adidas - Boys who prefer Adidas
= 20 - 19 = 1

- Total girls = Total students - Total boys
= 51 - 35 = 16

Now fill in the completed table:

```
Prefer Nike Prefer Adidas TOTAL
Boys 3 19 35
Girls 28 1 16
TOTAL 31 20 51
```

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Now let’s answer the questions.

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6. What is the relative frequency that a boy was polled?

Relative frequency = (Number of boys) / (Total students)
= 35 / 51 ≈ 0.686 or 68.6%

✔ Answer: ≈ 0.686

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7. What is the relative frequency of selecting a boy out of the people who prefer Adidas shoes?

This is a conditional probability: Among those who prefer Adidas, what proportion are boys?

Number of people who prefer Adidas = 20
Number of boys who prefer Adidas = 19

Relative frequency = 19 / 20 = 0.95 or 95%

✔ Answer: 0.95

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8. Does there appear to be an association between being a boy and preferring Adidas shoes?

Yes. From the data:
- 19 out of 20 people who prefer Adidas are boys → very strong tendency
- Only 1 girl prefers Adidas
- This suggests that boys are much more likely to prefer Adidas than girls.

✔ Answer: Yes, there appears to be a strong association — most Adidas wearers are boys.

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9. What is the relative frequency that a girl was polled?

Total girls = 16
Total students = 51

Relative frequency = 16 / 51 ≈ 0.314 or 31.4%

✔ Answer: ≈ 0.314

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10. What is the relative frequency of selecting a girl out of the people who prefer Adidas shoes?

From earlier:
- People who prefer Adidas = 20
- Girls who prefer Adidas = 1

Relative frequency = 1 / 20 = 0.05 or 5%

✔ Answer: 0.05

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11. Does there appear to be an association between being a girl and preferring Adidas shoes?

No. Only 1 out of 20 Adidas wearers is a girl → very low.

Also, girls are much more likely to prefer Nike (28 out of 16 girls total → all but one girl prefer Nike).

So, girls are not associated with preferring Adidas — in fact, they are strongly associated with preferring Nike.

✔ Answer: No, there does not appear to be an association; girls are unlikely to prefer Adidas.

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12. Write a sentence that summarizes what the data in the poll shows.

✔ Answer: The data shows that boys are much more likely to prefer Adidas shoes, while girls overwhelmingly prefer Nike shoes.

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✔ Final Answers Summary:

6. 0.686
7. 0.95
8. Yes, there is a strong association between being a boy and preferring Adidas.
9. 0.314
10. 0.05
11. No, there does not appear to be an association between being a girl and preferring Adidas.
12. The data shows that boys are much more likely to prefer Adidas shoes, while girls overwhelmingly prefer Nike shoes.

Let me know if you'd like this formatted as a printable answer sheet!