Treatment factor $T$ has levels. There are two blocking factors $B$ and $C$, each with levels, and a Latin square is used for the experimental design. Assume the following linear model:
$Y_{ijk} = \mu + \alpha_i + \beta_j + \tau_k + \epsilon_{ijk} \qquad (i, j, k = 1, \ldots, ),$
where $\mu$ is the overall mean, $\alpha_1, \ldots, \alpha_{}$ are the effects of the levels of the blocking factor $B$, $\beta_1, \ldots, \beta_{}$ are the effects of the levels of the blocking factor $C$, $\tau_1, \ldots, \tau_{}$ are the effects of the levels of the treatment factor $T$, and the $\epsilon_{ijk}$ are assumed to be independent $N(0, \sigma^2)$ random variables.

Part a) How many observations are there on level 1 of $T$ in the experiment?

Part b) How many df are there for residuals?

Part c) Consider the contrast $\kappa = \tau_{1} - \tau_{2}$. The variance of its least squares estimator is of the form $v \sigma^2$. Enter $v$ to 3 decimal places.

Part d) Suppose we test the null hypothesis $H_0: \kappa = 0$ against the alternative $H_a: \kappa \ne 0$ using the test statistic $| \hat{\tau} / \mbox{se}(\hat{\tau}) |$. How large does the test statistic have to be to reject $H_0$ at significance level 1%? Enter you answer to 3 decimal places.