Invert a two-sided test without imposing integer means

A random sample of 50 packets of ‘Nilo Bar’ snacks is weighed and the mass, $x$ grams, is recorded. The results are summarised by

$\sum(x-150)=-250,\qquad\sum(x-150)^2=3000.$

The population mean mass is $\mu$ grams. A test is carried out at the 1% significance level with the following hypotheses:

$H_0:\mu=\mu_0,\qquad H_1:\mu\ne\mu_0.$

Given that $H_0$ is rejected in favour of $H_1$, find the set of possible values of $\mu_0$.5 marks