I cannot find a formula for estimating coefficients ($a$ and $b$) of ANOVA model given by: $$\operatorname{weight} = a \cdot \operatorname{sex} + b + \epsilon$$ where $\operatorname{sex}=1$ means male and $\operatorname{sex}=0$ means female. The following table is provided
\begin{array}{|c|c|c|c|} \hline \text{sex}& \text{amount} & \text{mean weight} & \text{std} \\ \hline \text{male} & 94 & 31.7 &2.62\\ \hline \text{female}& 83 & 25.23&2.00\\ \hline \end{array}
The following process works generally if your independent variable is binary and you can assume the usual assumptions for a linear regression.
Let $y = \text{weight}$ and $x = \text{sex}$. If you take an expectation of both sides conditioned on
sex, you have:$$ E[y | x = 0] = a*0 + b + E[\varepsilon | x = 0] , $$ $$ E[y | x = 1] = a*1 + b + E[\varepsilon | x = 1] . $$
If you assume $ E[\varepsilon | x ] = 0$ (exogeneity assumption of linear regression), then you have
$$ b = E[y | x = 0] , $$ $$ a = E[y | x = 1] - E[y | x = 0] . $$
Then, by the law of large numbers, a good estimator for the expectations is the relevant sample means:
$$ \hat{b} = \bar{y}_{x=0} , $$ $$ \hat{a} = \bar{y}_{x=1} - \bar{y}_{x=0} . $$
In other words, you can use the average weight of women as an estimator of $b$ and the difference in the average weight of men and women as an estimator of $a$.