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Answer: 11.2, β > 0
The test statistic for the slope coefficient is calculated as: t = (β₁ - β₀)/se(β₁) = (0.2043 - 0)/0.01828 = 11.1761 ≈ 11.2 Since n = 6, degrees of freedom = n - 2 = 4 For a one-tailed test at 0.5% significance with 4 degrees of freedom, the critical value t_{0.005,4} = 4.604 Since 11.1761 > 4.604, we reject H₀ and conclude that β₁ > 0 Therefore, the test statistic is 11.2 and the conclusion is β > 0.
Author: Nikitesh Somanthe
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Two variables have a linear relationship of the form: Y = -4.6 + 0.2043X The slope coefficient has a standard error equal to 0.01828. Carry out a test of H₀: β₁ = 0 vs Hₐ: β₁ > 0 at 0.5% significance, quoting the test statistic and the conclusion if the number of observations, n, is 6.
A
11.2, β > 0
B
11.2, β = 0
C
0.01828, β ≠ 0
D
11.2, β ≠ 0
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