Math Problem Statement
Solution
The task requires calculating the missing test statistic , interpreting the results, and determining the correct answer based on the given data.
Solution Steps:
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Identify the correlation coefficient : Given .
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Calculate the test statistic : The formula for is: Where is the sample size (number of data points).
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Determine the sample size: From the data, (5 data points).
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Substitute into the formula:
Simplify step-by-step:
Final computation:
So, .
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Interpret the P-value and significance level:
- Given , which is greater than , we fail to reject the null hypothesis.
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Conclusion:
- The correlation is not statistically significant.
- There is insufficient evidence to suggest a linear relationship between lemon imports and crash fatality rates.
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Correct Answer:
- The correct option is A: The results do not suggest any cause-effect relationship between the two variables.
Would you like me to explain any of the steps in more detail or clarify further? Here are some follow-up questions you might explore:
- What does a P-value signify in hypothesis testing?
- How is the test statistic used to assess significance?
- Why can correlation not imply causation?
- How does the sample size impact the test statistic?
- Can a negative still indicate a strong linear relationship?
Tip: Always examine whether the context and data make a causal relationship plausible before making conclusions!
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Math Problem Analysis
Mathematical Concepts
Linear correlation
Hypothesis testing
Statistical significance
Formulas
Correlation coefficient formula
Test statistic formula: t = r√(n-2) / √(1-r²)
Theorems
Null hypothesis testing
Significance level and P-value comparison
Suitable Grade Level
Grades 11-12 or introductory college statistics
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