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Regression Slope Hypothesis Test Interpretation

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A regression analysis of the relationship between temperature (x) and ice cream sales (y) produced the following output for the slope of the regression line: β̂ = 12.5, SE(β̂) = 2.1, t = 5.95, and p-value < 0.001. For a test of the hypotheses H₀: β = 0 versus Hₐ: β ≠ 0, which of the following is the correct conclusion?

A

Reject H₀; the slope equals 12.5 units

B

Reject H₀; there is a significant linear relationship

C

Fail to reject H₀; p-value exceeds significance level

D

Reject H₀; the slope differs from 12.5 units

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