Explanation:
The first step entails formulating the hypothesis:
H₀ : β₁ = 0 vs. Hₐ : β₁ ≠ 0
The test statistic for the slope coefficient takes the form: t₍α,n−2₎ = (β₁ − β₀) / se(β₁)
In this case, t₀.₀₂₅,₈ = (0.6566 − 0) / 0.0799 = 8.2177
(α = 5% / 2 since this is a 2-tailed test)
The critical 2-tailed values (t₀.₀₂₅,₈) are ±2.306
Our test statistic lies outside the non-rejection region (-2.306, 2.306). As such, we have sufficient evidence to reject the null hypothesis and conclude that the slope coefficient is statistically different than zero.
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Q.77 The estimated slope coefficient (β₁) for a certain stock is 0.6566, with a standard error equal to 0.0799. The sample had 10 observations, and a researcher wants to know if the slope coefficient is statistically different than zero. Using a 5% level of significance, what are the test statistic and the decision rule?
A
0.1217; do not reject H0
B
8.2177; do not reject H0
C
0.1217; reject H0
D
8.2177; reject H0
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