There are 3 strata. The total population size is $N = 400 = N_1+N_2+N_3$. From these, a total of $n = 30 = n_1+n_2+n_3$ units is sampled. Here, $N_1$ refers to the number of units in stratum 1 in the entire population and $n_1$ refers to the number of units in stratum 1 in the sample. The variances of the response variable in each stratum are $1.0, 1.5, 3.7$ respectively and the overall sample variance is $4.0$. Given that proportional allocation was used, explain why it is impossible to have a mean estimate of $7.0$ with a standard error of $0.5$ for the response variable.
My first thoughts were using the given stratum variances to calculate the standard error, but even this requires knowing the population weights ($W_h = \frac{n_h}{N_h}$ for proportional allocation). The mean, in addition to these, also requires knowing the mean in each stratum so I really don't know how to go about this. I am guessing that there is a way to use the overall sample variance to get some extra information about the population weights and the stratum means.