Financial Risk Manager Part 1

Explanation

This is a two-tailed hypothesis test for whether the slope coefficient is different from zero. The critical t-value for a 10% significance level (two-tailed) is given as 1.70.

From the confidence interval information provided:

• The confidence interval is [0.30, 1.60]
• The midpoint (which equals the slope coefficient estimate β̂) is calculated as: β̂ = (0.30 + 1.60)/2 = 0.95

Using the lower bound of the confidence interval formula: β̂ - Cₜ × SEE_β̂ = 0.30 Where Cₜ = 1.70 (critical value)

Solving for the standard error: 0.95 - 1.70 × SEE_β̂ = 0.30 1.70 × SEE_β̂ = 0.95 - 0.30 = 0.65 SEE_β̂ = 0.65 / 1.70 = 0.3824

The t-statistic is calculated as: t = β̂ / SEE_β̂ = 0.95 / 0.3824 ≈ 2.484

For a two-tailed test, the p-value is: p-value = 2 × P(T > |t|) = 2 × P(T > 2.484)

Looking up 2.484 in the t-distribution table (with appropriate degrees of freedom, though not specified, but typically large enough for normal approximation): P(T > 2.484) ≈ 0.0066

Thus, p-value = 2 × 0.0066 = 0.0132

This matches option A. The calculation shows that with a t-statistic of approximately 2.484, the p-value would be around 0.0132, which is less than 0.05 but greater than 0.01, indicating statistical significance at the 5% level but not at the 1% level.