= Solution
The fitted <Poisson regression> has
$$
Y_i\mid x_i\sim\operatorname{Pois}(\mu_i),
\qquad
\log\mu_i=\beta_0+\beta_1\log x_i,
$$
so that $\mu_i=e^{\beta_0}x_i^{\beta_1}$. Hypothesis $H_2$ requires both restrictions
$$
\beta_0=0,\qquad \beta_1=1,
$$
as well as the adequacy of the assumed <Poisson distribution>. The displayed interval addresses only the single slope restriction $\beta_1=1$. Even if the separate interval for the intercept also contains zero, separate one-parameter intervals do not implement the relevant <joint hypothesis test>, because the two coefficient estimators can be correlated. One should test $(\beta_0,\beta_1)=(0,1)$ jointly, for example by a <likelihood-ratio test>, and separately assess the Poisson goodness of fit. Thus the slope interval alone cannot decide whether $H_2$ is rejected at the $5\%$ level.
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