Listed below are annual data for various years. The data are weights (metric tons) of imported lemons and car crash fatality rates per 100,000 population. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using a= 0.05. Is there sufficient evidence to conclude there is a linear correlation between lemon imports and crash fatality rates? Do the results suggest that imported lemons cause car fatalities? Lemon Imports Crash Fatality Rate 230 15.8 265 15.7 359 15.5 482 15.3 530 14.9 What are the null and alternative hypotheses? O A. Ho: p0 H: p0 OB. Ho: p0 H:p=0 OC. Ho: p0 OD. Ho: p=0 H:p<0 H:p>0 Construct a scatterplot. Choose the correct graph below. O A. OB. Oc. OD. 174 174 174 174 16 16- 16- 16- Le 15 15- 15- 15 to 14 14+ 14- 14+ 200 400 600 200 400 6ó0 200 400 so0 200 400 G00 The linear correlation coefficient is r" (Round to three decimal places as needed.) The test statistic is t= (Round to three decimal places as needed.) The P-value is (Round to three decimal places as needed.) Because the P-value is V than the significance level 0.05, there v sufficient evidence to support the claim that there is a linear correlation between lemon imports and crash fatality rates for a significance level of a 0.05. Do the results suggest that imported lemons cause car fatalities? O A. The results suggest that imported lemons cause car fatalities. O B. The results suggest that an increase in imported lemons causes car fatality rates to remain the same. OC. The results suggest that an increase in imported lemons causes in an increase in car fatality rates. O D. The results do not suggest any cause-effect relationship between the two variables.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Author:Carter
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Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 16HP
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# Lemons and Car Fatalities: Analyzing Correlation

## Data Overview
The table below provides annual data, showing the weight (in metric tons) of imported lemons and the car crash fatality rates per 100,000 population.

| Lemon Imports (metric tons) | Crash Fatality Rate (per 100,000) |
|-----------------------------|----------------------------------|
| 230                         | 15.8                             |
| 265                         | 15.7                             |
| 359                         | 15.5                             |
| 482                         | 15.3                             |
| 530                         | 14.9                             |

## Hypothesis Testing
To determine if there is a linear correlation between lemon imports and crash fatality rates, we set up the following hypotheses:

- **A.**
  - Null Hypothesis (H₀): ρ = 0
  - Alternative Hypothesis (H₁): ρ ≠ 0

- **B.**
  - Null Hypothesis (H₀): ρ ≠ 0
  - Alternative Hypothesis (H₁): ρ = 0

- **C.**
  - Null Hypothesis (H₀): ρ = 0
  - Alternative Hypothesis (H₁): ρ > 0

- **D.**
  - Null Hypothesis (H₀): ρ = 0
  - Alternative Hypothesis (H₁): ρ < 0

## Scatterplot Construction
Select and construct the appropriate scatterplot from the options below:

- **A.** Scatterplot with a slight negative trend
- **B.** Scatterplot with points scattered randomly
- **C.** Scatterplot with a clear negative trend
- **D.** Scatterplot with an upward trend

## Statistical Analysis
Determine the statistical values:

1. The linear correlation coefficient \( r \) is: [Enter value]
   - (Round to three decimal places as needed.)

2. The test statistic \( t \) is: [Enter value]
   - (Round to three decimal places as needed.)

3. The P-value is: [Enter value]
   - (Round to three decimal places as needed.)

## Conclusion
Based on the P-value:
- If the P-value is [Choose: less/greater] than the significance level of 0.05, there is [sufficient/
Transcribed Image Text:# Lemons and Car Fatalities: Analyzing Correlation ## Data Overview The table below provides annual data, showing the weight (in metric tons) of imported lemons and the car crash fatality rates per 100,000 population. | Lemon Imports (metric tons) | Crash Fatality Rate (per 100,000) | |-----------------------------|----------------------------------| | 230 | 15.8 | | 265 | 15.7 | | 359 | 15.5 | | 482 | 15.3 | | 530 | 14.9 | ## Hypothesis Testing To determine if there is a linear correlation between lemon imports and crash fatality rates, we set up the following hypotheses: - **A.** - Null Hypothesis (H₀): ρ = 0 - Alternative Hypothesis (H₁): ρ ≠ 0 - **B.** - Null Hypothesis (H₀): ρ ≠ 0 - Alternative Hypothesis (H₁): ρ = 0 - **C.** - Null Hypothesis (H₀): ρ = 0 - Alternative Hypothesis (H₁): ρ > 0 - **D.** - Null Hypothesis (H₀): ρ = 0 - Alternative Hypothesis (H₁): ρ < 0 ## Scatterplot Construction Select and construct the appropriate scatterplot from the options below: - **A.** Scatterplot with a slight negative trend - **B.** Scatterplot with points scattered randomly - **C.** Scatterplot with a clear negative trend - **D.** Scatterplot with an upward trend ## Statistical Analysis Determine the statistical values: 1. The linear correlation coefficient \( r \) is: [Enter value] - (Round to three decimal places as needed.) 2. The test statistic \( t \) is: [Enter value] - (Round to three decimal places as needed.) 3. The P-value is: [Enter value] - (Round to three decimal places as needed.) ## Conclusion Based on the P-value: - If the P-value is [Choose: less/greater] than the significance level of 0.05, there is [sufficient/
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