Referring to the data in question 2 and the following conditional distributions, is there a potential  association between age and toy preference?

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Referring to the data in question 2 and the following conditional distributions, is there a potential  association between age and toy preference?

A study was conducted involving a sample of 337 children, who were asked about their favorite toys among the following options: Barbies, cars, stuffed animals, and building blocks. The children were divided into three age groups: 1-3, 4-6, and 7-9. The table below presents the results of this study:

| Age Group | Barbies | Cars | Stuffed Animals | Blocks | Total |
|-----------|---------|------|----------------|--------|-------|
| 1 to 3    | 2       | 17   | 15             | 4      | 38    |
| 4 to 6    | 20      | 35   | 24             | 45     | 124   |
| 7 to 9    | 59      | 70   | 14             | 32     | 175   |
| **Total** | **81**  | **122** | **53**        | **81** | **337** |

### Analysis:

- **Age Group 1 to 3**: Bars show that cars are the most popular toy with 17 kids selecting them, followed by stuffed animals (15), Barbies (2), and blocks (4).
- **Age Group 4 to 6**: The preference shifts, with blocks being the most favored (45), followed by cars (35), Barbies (20), and stuffed animals (24).
- **Age Group 7 to 9**: Cars gain more popularity with 70 children choosing them, followed by Barbies (59), blocks (32), and stuffed animals (14).

Overall, when consolidating data across all age groups, cars are the favorite toy, chosen by 122 children, followed by both Barbies and blocks, each selected by 81 children, while stuffed animals are the least favored with 53 votes.
Transcribed Image Text:A study was conducted involving a sample of 337 children, who were asked about their favorite toys among the following options: Barbies, cars, stuffed animals, and building blocks. The children were divided into three age groups: 1-3, 4-6, and 7-9. The table below presents the results of this study: | Age Group | Barbies | Cars | Stuffed Animals | Blocks | Total | |-----------|---------|------|----------------|--------|-------| | 1 to 3 | 2 | 17 | 15 | 4 | 38 | | 4 to 6 | 20 | 35 | 24 | 45 | 124 | | 7 to 9 | 59 | 70 | 14 | 32 | 175 | | **Total** | **81** | **122** | **53** | **81** | **337** | ### Analysis: - **Age Group 1 to 3**: Bars show that cars are the most popular toy with 17 kids selecting them, followed by stuffed animals (15), Barbies (2), and blocks (4). - **Age Group 4 to 6**: The preference shifts, with blocks being the most favored (45), followed by cars (35), Barbies (20), and stuffed animals (24). - **Age Group 7 to 9**: Cars gain more popularity with 70 children choosing them, followed by Barbies (59), blocks (32), and stuffed animals (14). Overall, when consolidating data across all age groups, cars are the favorite toy, chosen by 122 children, followed by both Barbies and blocks, each selected by 81 children, while stuffed animals are the least favored with 53 votes.
**Conditional Distributions of Toy Preference by Age Group**

The table below illustrates the conditional distributions that indicate the potential association between age and toy preference. 

| Age Group | Barbies | Cars | Stuffed Animals | Blocks | Total |
|-----------|---------|------|-----------------|--------|-------|
| 1 to 3    | 0.05    | 0.45 | 0.39            | 0.11   | 1     |
| 4 to 6    | 0.16    | 0.28 | 0.19            | 0.36   | 1     |
| 7 to 9    | 0.24    | 0.40 | 0.11            | 0.18   | 1     |
| Total     | 0.24    | 0.36 | 0.16            | 0.24   | 1     |

**Analysis of Potential Association:**

The table provides a breakdown of toy preferences among different age groups. Each row sums to a total of 1, representing the total distribution for that specific age group across the four toy categories. 

**Question:**
Is there an association between age and toy preference based on the conditional distributions?

**Options:**
- Yes, because the conditional distributions differ from each other.
- No, because the conditional distributions are the same.

This data helps analyze whether certain age groups show a stronger preference for certain types of toys, which could indicate a trend or association between age and toy choice.
Transcribed Image Text:**Conditional Distributions of Toy Preference by Age Group** The table below illustrates the conditional distributions that indicate the potential association between age and toy preference. | Age Group | Barbies | Cars | Stuffed Animals | Blocks | Total | |-----------|---------|------|-----------------|--------|-------| | 1 to 3 | 0.05 | 0.45 | 0.39 | 0.11 | 1 | | 4 to 6 | 0.16 | 0.28 | 0.19 | 0.36 | 1 | | 7 to 9 | 0.24 | 0.40 | 0.11 | 0.18 | 1 | | Total | 0.24 | 0.36 | 0.16 | 0.24 | 1 | **Analysis of Potential Association:** The table provides a breakdown of toy preferences among different age groups. Each row sums to a total of 1, representing the total distribution for that specific age group across the four toy categories. **Question:** Is there an association between age and toy preference based on the conditional distributions? **Options:** - Yes, because the conditional distributions differ from each other. - No, because the conditional distributions are the same. This data helps analyze whether certain age groups show a stronger preference for certain types of toys, which could indicate a trend or association between age and toy choice.
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