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Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.025 significance level. (Round intermediate calculations and final answer to 3 decimal places.)

H0: ρ ≤ 0; H1: ρ > 0 Reject H0 if t > 2.101         t =	


The Pearson correlation coefficient \( r \) between Wattage and Area is approximately \( 0.151 \), indicating a weak positive correlation. The calculated t-statistic is approximately \( 0.648 \).

Given that we reject the null hypothesis \( H_0 \) if \( t > 2.101 \), and since \( 0.648 \) is less than \( 2.101 \), we **fail to reject** the null hypothesis \( H_0 \). This means there is insufficient evidence to conclude that the correlation coefficient is greater than zero at the \( 0.025 \) significance level.

Would you like further details or have any questions?

Here are 5 related questions you might want to explore:
1. What factors could explain the weak correlation between wattage and area?
2. How does changing the significance level affect the outcome of the hypothesis test?
3. Can we explore different methods to model the relationship between wattage and area?
4. How would the correlation coefficient change if we removed outliers from the dataset?
5. What is the interpretation of the correlation coefficient and its limitations?

**Tip:** Always check for outliers or potential data entry errors when dealing with real-world data, as they can significantly affect correlation analysis.

Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.025 significance level. H0: ρ ≤ 0; H1: ρ > 0 Reject H0 if t > 2.101.

Test the hypothesis for correlation between heater wattage and the area it covers. Using a significance level of 0.025 and calculating the Pearson correlation coefficient, find out if the correlation is significant.

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