The accompanying table lists the ages of acting award winners matched by the years in which the awards were won. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Should we expect that there would be a correlation? Use a significance level of a = 0.01. H Click the icon to view the ages of the award winners. Construct a scatterplot. Choose the correct graph below. OA. OB. Oc. OD. Best Actress (years) Rest Actress (years) Best Astress (years Best Astress (vears) The linear correlation coefficient is rO (Round to three decimal places needed.) Determine the null and alternative hypotheses. Họ: p H: p O (Type integers or decimals. Do not round.) The test statistic ist (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) Because the P-value of the linear correlation coefficient is V the significance level, there sufficient evidence to support the claim that there is a linear correlation between the ages of Best Actresses and Best Actors. Should we expect that there would be a correlation? O A. No, because Best Actors and Best Actresses typically appear in different movies, so we should not expect the ages to be correlated. O B. Yes, because Best Actors and Best Actresses are typically the same age OC. Yes, because Best Actors and Best Actresses typically appear in the same movies, so we should expect the ages to be correlated. OD. No, because Best Actors and Best Actresses are not typically the same age.

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### Age Distribution of Best Actor and Best Actress Award Winners

The table below displays the ages of winners for the "Best Actress" and "Best Actor" categories. This data offers insight into the age demographics commonly seen among award recipients.

| Best Actress | 29 | 29 | 30 | 58 | 33 | 32 | 47 | 30 | 63 | 22 | 45 | 54 |
|--------------|----|----|----|----|----|----|----|----|----|----|----|----|
| Best Actor   | 43 | 37 | 37 | 45 | 52 | 46 | 57 | 52 | 39 | 55 | 43 | 32 |

**Analysis:**
- The ages of Best Actress winners range from 22 to 63, showing a significant variation which indicates diverse age representation among winners.
- The ages of Best Actor winners range from 32 to 57, suggesting a slightly older age bracket compared to the actresses. 

This comparison can help explore industry trends and perceptions regarding age.
Transcribed Image Text:### Age Distribution of Best Actor and Best Actress Award Winners The table below displays the ages of winners for the "Best Actress" and "Best Actor" categories. This data offers insight into the age demographics commonly seen among award recipients. | Best Actress | 29 | 29 | 30 | 58 | 33 | 32 | 47 | 30 | 63 | 22 | 45 | 54 | |--------------|----|----|----|----|----|----|----|----|----|----|----|----| | Best Actor | 43 | 37 | 37 | 45 | 52 | 46 | 57 | 52 | 39 | 55 | 43 | 32 | **Analysis:** - The ages of Best Actress winners range from 22 to 63, showing a significant variation which indicates diverse age representation among winners. - The ages of Best Actor winners range from 32 to 57, suggesting a slightly older age bracket compared to the actresses. This comparison can help explore industry trends and perceptions regarding age.
The text describes an educational task related to correlational statistics using fictional data about acting award winners. Here's a transcription and explanation suitable for an educational website:

---

**Correlation Exercise with Acting Award Winners' Ages**

The accompanying table lists the ages of acting award winners matched by the years in which the awards were won. The task involves constructing a scatterplot, calculating the linear correlation coefficient (r), and determining the P-value for r. Finally, you must assess whether there is sufficient evidence to support a claim of linear correlation between the two variables using a significance level of α = 0.01.

### Instructions:

1. **Scatterplot Construction**
   - Choose the correct scatterplot from four options:
     - **Option A**: Indicates a moderate positive correlation.
     - **Option B**: Shows no apparent correlation.
     - **Option C**: Illustrates a negative correlation.
     - **Option D**: Displays a moderate positive correlation with less variability than Option A.

2. **Linear Correlation Coefficient (r)**
   - Compute the value of r to three decimal places.
   - **Enter the Value**: A box is provided for input.

3. **Determine Hypotheses**
   - Null Hypothesis (H₀): There is no correlation (ρ = 0).
   - Alternative Hypothesis (H₁): There is a correlation (ρ ≠ 0).

4. **Test Statistic and P-value**
   - Calculate the test statistic, t, and round it to two decimal places, providing an answer box for input.
   - Compute the P-value, rounding to three decimal places, with another answer box for input.

5. **Conclusion Based on P-value**
   - Compare the P-value against the significance level to decide:
     - If there is sufficient evidence to claim a linear correlation.
   - Multiple-choice for reasoning:
     - **A**: No correlation due to typical age differences in separate movies.
     - **B**: Correlation likely due to similar age range.
     - **C**: Expectation of correlation from concurrent movie releases.
     - **D**: Expectation of no correlation due to disparate ages.

### Key Considerations:

- Understand the implications of r values close to -1, 0, or 1.
- P-value interpretation relative to α = 0.01.
- Contextual reasoning behind actor and actress ages in movies.

This task helps in understanding statistical hypothesis testing
Transcribed Image Text:The text describes an educational task related to correlational statistics using fictional data about acting award winners. Here's a transcription and explanation suitable for an educational website: --- **Correlation Exercise with Acting Award Winners' Ages** The accompanying table lists the ages of acting award winners matched by the years in which the awards were won. The task involves constructing a scatterplot, calculating the linear correlation coefficient (r), and determining the P-value for r. Finally, you must assess whether there is sufficient evidence to support a claim of linear correlation between the two variables using a significance level of α = 0.01. ### Instructions: 1. **Scatterplot Construction** - Choose the correct scatterplot from four options: - **Option A**: Indicates a moderate positive correlation. - **Option B**: Shows no apparent correlation. - **Option C**: Illustrates a negative correlation. - **Option D**: Displays a moderate positive correlation with less variability than Option A. 2. **Linear Correlation Coefficient (r)** - Compute the value of r to three decimal places. - **Enter the Value**: A box is provided for input. 3. **Determine Hypotheses** - Null Hypothesis (H₀): There is no correlation (ρ = 0). - Alternative Hypothesis (H₁): There is a correlation (ρ ≠ 0). 4. **Test Statistic and P-value** - Calculate the test statistic, t, and round it to two decimal places, providing an answer box for input. - Compute the P-value, rounding to three decimal places, with another answer box for input. 5. **Conclusion Based on P-value** - Compare the P-value against the significance level to decide: - If there is sufficient evidence to claim a linear correlation. - Multiple-choice for reasoning: - **A**: No correlation due to typical age differences in separate movies. - **B**: Correlation likely due to similar age range. - **C**: Expectation of correlation from concurrent movie releases. - **D**: Expectation of no correlation due to disparate ages. ### Key Considerations: - Understand the implications of r values close to -1, 0, or 1. - P-value interpretation relative to α = 0.01. - Contextual reasoning behind actor and actress ages in movies. This task helps in understanding statistical hypothesis testing
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