Police sometimes measure shoe prints at crime scenes so that they can learn something about criminals. Listed below are shoe print lengths, foot lengths, and heights of males. 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. Based on these results, does it appear that police can use a shoe print length to estimate the height of a male? Use a significance level of a = 0.05. Shoe Print (cm) Foot Length (cm) Height (cm) ▼ 29.6 29.6 30.5 30.7 27.4 25.2 26.3 27.0 27.0 24.6 180.7 182.7 189.9 168.6 176.3 Ho: P| H₁: P (Type integers or decimals. Do not round.) The test statistic is t=. (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) ← the significance level, there Because the P-value of the linear correlation coefficient is between shoe print lengths and heights of males. Based on these results, does it appear that police can use a shoe print length to estimate the height of a male? O A. No, because shoe print length and height appear to be correlated. O B. Yes, because shoe print length and height appear to be correlated. O C. Yes, because shoe print length and height do not appear to be correlated. O D. No, because shoe print length and height do not appear to be correlated. sufficient evidence to support the claim that there is a linear correlation

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## Understanding Correlation in Forensic Science: Shoe Prints and Height

Police sometimes measure shoe prints at crime scenes to gain insights about criminals. Listed below are shoe print lengths, foot lengths, and heights of males. This study examines whether there is a linear correlation between these variables. A significance level of α = 0.05 is used.

### Data Table

| Shoe Print (cm) | Foot Length (cm) | Height (cm) |
|-----------------|------------------|-------------|
| 29.6            | 25.2             | 180.7       |
| 29.6            | 26.3             | 182.7       |
| 30.5            | 27.0             | 189.9       |
| 30.7            | 27.0             | 168.6       |
| 27.4            | 24.6             | 176.3       |

### Hypothesis Testing

1. **Null Hypothesis (H₀):** ρ = 0  
   (There is no linear correlation between shoe print lengths and heights.)

2. **Alternative Hypothesis (H₁):** ρ ≠ 0  
   (There is a linear correlation between shoe print lengths and heights.)

### Statistical Analysis

- **Test Statistic (t):** Fill in the calculated value.
- **P-Value:** Fill in the estimated probability.

### Interpretation

Based on the P-value:

- If the P-value of the linear correlation coefficient is _____ the significance level, there _____ sufficient evidence to support the claim that there is a linear correlation between shoe print lengths and heights of males.

### Conclusion

- **Option A:** No, because shoe print length and height appear to be correlated.
- **Option B:** Yes, because shoe print length and height appear to be correlated.
- **Option C:** Yes, because shoe print length and height do not appear to be correlated.
- **Option D:** No, because shoe print length and height do not appear to be correlated.

Decide whether police can use a shoe print length to estimate the height of a male based on these results.
Transcribed Image Text:## Understanding Correlation in Forensic Science: Shoe Prints and Height Police sometimes measure shoe prints at crime scenes to gain insights about criminals. Listed below are shoe print lengths, foot lengths, and heights of males. This study examines whether there is a linear correlation between these variables. A significance level of α = 0.05 is used. ### Data Table | Shoe Print (cm) | Foot Length (cm) | Height (cm) | |-----------------|------------------|-------------| | 29.6 | 25.2 | 180.7 | | 29.6 | 26.3 | 182.7 | | 30.5 | 27.0 | 189.9 | | 30.7 | 27.0 | 168.6 | | 27.4 | 24.6 | 176.3 | ### Hypothesis Testing 1. **Null Hypothesis (H₀):** ρ = 0 (There is no linear correlation between shoe print lengths and heights.) 2. **Alternative Hypothesis (H₁):** ρ ≠ 0 (There is a linear correlation between shoe print lengths and heights.) ### Statistical Analysis - **Test Statistic (t):** Fill in the calculated value. - **P-Value:** Fill in the estimated probability. ### Interpretation Based on the P-value: - If the P-value of the linear correlation coefficient is _____ the significance level, there _____ sufficient evidence to support the claim that there is a linear correlation between shoe print lengths and heights of males. ### Conclusion - **Option A:** No, because shoe print length and height appear to be correlated. - **Option B:** Yes, because shoe print length and height appear to be correlated. - **Option C:** Yes, because shoe print length and height do not appear to be correlated. - **Option D:** No, because shoe print length and height do not appear to be correlated. Decide whether police can use a shoe print length to estimate the height of a male based on these results.
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